For as the Father has life in himself, so he has granted the Son also to have life in himself. (John 5:26, NIV)
How do trinitarians explain the fact that the Father has granted life to the Son?
The "begetting" here is understood in an eternal sense, and is not a matter of being made or created. The creeds phrase it as eternally begetting (fathering), or pretemporal begetting, or an eternal proceeding from. And they are explicit in that it is not a matter of being made or created.
From the Athanasian Creed,
The Son is of the Father alone; not made, nor created, but begotten.
So there is One Father, not Three Fathers; one Son, not Three Sons; One Holy Ghost, not Three Holy Ghosts. And in this Trinity none is afore or after Other, None is greater or less than Another, but the whole Three Persons are Co-eternal together, and Co-equal.
And from the Nicene Creed,
And in one Lord Jesus Christ, the only begotten Son of God, and born of the Father before all ages. (God of God) light of light, true God of true God. Begotten not made, consubstantial to the Father, by whom all things were made.
The Son proceeds from The Father and is therefore of the same eternal substance. This differs from created entities, which are different in "substance" from their creator. The Father is the eternal cause of the Son; but the Son is not created or a distinct substance from the Father. The Father and the Son, with the Holy Spirit, are one in being.
All Scripture is quoted from the New Revised King James Version
you are confusing the material with the immaterial. The Trinity (God) is Deity. And in :
John 5:26 For as the Father hath life in himself; so hath he given to the Son to have life in himself;
What Jesus is saying is that the father has given *his physical body*life within itself. That is why Jesus said:
John 10:17 and 18
Therefore doth my Father love me, because I lay down my life, that I might take it again. No man taketh it from me, but I lay it down of myself. I have power to lay it down, and I have power to take it again. This commandment have I received of my Father.
Jesus life, death, and resurrection, were all commanded by God the father.
Where your confusion comes in is that you unconsciously attribute materialistic properties to God. We must understand that God is something beyond the intelligence of man.
Isaiah 55:9 For as the heavens are higher than the earth, so are my ways higher than your ways, and my thoughts than your thoughts.
We will never completely know God until we meet him face to face.
John 5:26 (NIV)
26 For as the Father has life in himself, so he has granted the Son also to have life in himself.
The Son is subordinate to the Father in terms of role while at the same time equal with the Father in terms of nature.
This giving of life or nature is not like I'm giving you a plate of pasta or as if i'm handing over a book to you. Rather, to give one's nature is entirely different. In Humans, parents give their nature or pass on their genes into their offspring by gestation through intercourse.
It is shown that the Father gave his Son the same life or nature he has by means of begetting.
The Son is begotten from the Father ( 1 John 5:18). In fact, he is the only begotten from the Father ( John 1:14, 18; 3:16).
It just so happens that the Scriptures are silent about how it happened. What's important is that we know that the Son, due to his begetting from the Father, is consubstantial (same in nature) with the Father.
John 10:28-30 (NIV)
28 I give them eternal life, and they shall never perish; no one will snatch them out of my hand. 29 My Father, who has given them to me, is greater than all; no one can snatch them out of my Father’s hand. 30 I and the Father are one.”
Life - the state of being alive due to one's nature (i.e. existence/ being).
To beget means to produce someone to have one's nature.
The passage more accurately says the Father "granted also to the Son to have life in himself" NWT
So what the passage says the Father granted the Son is not simply to "have life" but to "have life in himself."
In order to understand what it means for the Father to grant the Son to have life in himself we must understand what it means for the Father to have life in himself. After all it is the Father's having of "life in himself" that the passage affirms the Son has been granted by the Father in common with the Father.
To "have life in oneself" is not the same as to "have life." All living things have life but none has life in itself.
The phrase also does not mean to be created or generated otherwise the statement "the Father has life in himself" would then mean that God the Father creates or generates himself, which is absolutely wrong as he is not generated; he simply is.
To have life in oneself means to be self-sustaining, self-sufficient, self-existent. It means to need nothing external to yourself to exist. Only God has such a quality and class of life. He alone needs no one to exist.
So when Jesus says in the passage that the Father granted the Son to have life in himself it was another veiled reference to his Godhood.
He was invariably saying he is a carbon copy of the Father in quality and class of life. The Father willed himself to be replicated in the Son and so the Son exists separate from the Father but with self-existent life exactly like the Father. Heb.1:3 describes the Son as "the EXACT representation of his (the Father's) very being" NWT
Jesus' sonhood is not a mere title or office, it is actual. He is the Father's exact replica, sourced from the Father's very essence and willed at sourcing and thereafter to be self-sufficient and existent.
His sourcing from the Father does not time his life by the action of the sourcing just as a candle light taken from a previous one does not have its existence timed at the point of taking, rather it is timed by the parent fire life. For it is simply the parent fire replicated unto a new candle without losing itself.
His replication also does not increase the quantity of the Father's essence as growing a maize cob from a maize seed multiplies the count of the original seed. It is the infinite nature of the Father's substance that makes this peculiarly so. Just as infinity cannot be increased in quantity by the addition or multiplication of itself by itself, so also the infinite God cannot be increased by his replication of himself in the Son or in any other. He could multiply himself as many times as he wills without increment to his essence.
I would read it as "Has authorised the Son to have life in Himself"....Whilst the Persons of the Holy Trinity are each God in essence, yet they are separate Persons with various things they do. So the Father sent the Son and the Son took to Himself a human nature (thus Jesus Christ is two natures in one person). But it was not the Father or the Holy Spirit Who took on a human nature, only the Son. We might say that in the Trinity, the Father authorised the Son to become a man and in perfect eternal harmony, the three agreed that it should be so. Likewise that the Father should send the Son and after the resurrection of the Lord, that they should send the Holy Spirit at Pentecost to indwell believers. Also see Matthew Henry's comments about this.
For a further explanantion of the Trinity pls see What is the doctrine of the Trinity?
The NIV is distorting the Greek text here.
The word translated as "grant" is δίδωμι (didōmi), which can mean both to simply give something to someone or to give in the sense of allow or enable. The meaning depends on the context, and the NIV seems to ignore the context of the preceding verse:
Very truly I tell you, a time is coming and has now come when the dead will hear the voice of the Son of God and those who hear will live.
The meaning of verse 26 is not that the Father somehow gave life to the Son, but, in keeping with the preceding verse, gave to the Son those who would have life in Him.
The verses that follow actually would have been a better argument against the Trinity:
26For as the Father has life in himself, so he has granted the Son also to have life in himself.
27And he has given him authority to judge because he is the Son of Man.
28“Do not be amazed at this, for a time is coming when all who are in their graves will hear his voice
In other words, according to v. 27, without the Father giving Him the authority, the Son would not have the authority to judge.
The NIV is following the punctuation that is specified in the Nestle-Aland "Critical Text" (the original texts had no punctuation whatsoever):
ὥσπερ γὰρ ὁ πατὴρ ἔχει ζωὴν ἐν ἑαυτῷ, οὕτως καὶ τῷ υἱῷ ἔδωκεν ζωὴν ἔχειν ἐν ἑαυτῷ.
καὶ ἐξουσίαν ἔδωκεν αὐτῷ κρίσιν ποιεῖν, ὅτι υἱὸς ἀνθρώπου ἐστίν.
μὴ θαυμάζετε τοῦτο, ὅτι ἔρχεται ὥρα ἐν ᾗ πάντες οἱ ἐν τοῖς μνημείοις ἀκούσουσιν τῆς φωνῆς αὐτοῦ
But this interpretation of the text was expressly condemned in the 4th century as heretical, for the reason stated above. (See, e.g., John Chrysostom, Homily XXXIX on John). An alternate reading is:
ὥσπερ γὰρ ὁ πατὴρ ἔχει ζωὴν ἐν ἑαυτῷ, οὕτως ἔδωκε καὶ τῷ υἱῷ ζωὴν ἔχειν ἐν ἑαυτῷ·
καὶ ἐξουσίαν ἔδωκεν αὐτῷ καὶ κρίσιν ποιεῖν. ὅτι υἱὸς ἀνθρώπου ἐστί,
μὴ θαυμάζετε τοῦτο· ὅτι ἔρχεται ὥρα ἐν ᾗ πάντες οἱ ἐν τοῖς μνημείοις ἀκούσονται τῆς φωνῆς αὐτοῦ
For even as the Father has life in Himself, so He also gave to the Son to have life in Himself,
and He also gave to Him authority to execute judgment. That He is Son of Man,
cease marveling at this; for an hour is coming in which all those in the grave shall hear His voice.
In other words, marvel at the fact that Christ is (also) Son of Man and not, as the other reading suggests, that God decided to give Him authority to execute judgment. Nonetheless, almost all modern English language translations - as well as the KJV and NKJV - opt for something like the CT scheme.
We should start from the basic theistic notion of absolute divine simplicity: God (each of the divine Persons) does not have a life, intellect, will, power, goodness, or any other attribute, which is different from the divine essence, which in turn is identical to the (one and only) Subsistent Act of Being (Esse Subsistens) .
Thus, each of the divine Persons Is the Subsistent Act of Being, the Father as Subsistent Paternity (for St. Thomas Aquinas) or as Subsistent Fontal Plenitude and Paternity (for St. Bonaventure of Bagnoregio), the Son as Subsistent Filiation and the Holy Spirit as Subsistent Passive Spiration, so that each of the divine Persons can apply to Himself the Name of God in the first person "I Am" (Ex 3:14), which Jesus actually did several times in John's Gospel .
Having this in mind, we can restate the passage in ontological terms:
"For as the Father has life in Himself, so He has granted the Son also to have life in Himself." = For as the Father Is the (one and only) Subsistent Act of Being, so He has granted the Son also to Be the (one and only) Subsistent Act of Being.
 To state explicitly this identity is relevant only for those who hold the metaphysics-level notion of the real distinction between the essence and the act of being (a.k.a. existence) of contingent entities, i.e. for thomists.
 When dealing with matters of divine ontology I capitalize the verb "to be" when its subject is a divine Person, to distinguish Subsistent Being from contingent being.