My first reaction is that this is simply not the accepted understanding of the passage, and that this understanding can only come from a person determined to find fault in it. But that hardly seems to do it justice, so here's a better, more complete answer:
One obvious response to the idea that Matthew 8:20 refers to Jesus acknowledging that He isn't divine is that it's odd that a Jew would not know their own Scripture. Although the phrase "Son of Man" was a phrase of "humilation and debasement", the phrase actually points to His divinity, as the foretold one, right from the book of Daniel 7:13(KJV)
I saw in the night visions, and, behold, one like the Son of man came
with the clouds of heaven, and came to the Ancient of days, and they
brought him near before him.
Moreso, the fact that Jesus would come in humility is right out of Psalm 8:5.
For thou hast made him a little lower than the angels, and hast
crowned him with glory and honour.
As for why Jesus would want to discourage this person from following Him, a common understanding is that this scribe expected material gain, and Jesus was just giving him a realiztic expectation of the life he would lead if he followed Christ.
From Gill's Exposition of the Entire Bible
...So that though he was Lord of all, as being the mighty God; yet as
"the son of man", a phrase, expressive both of the truth and meanness
of his human nature, the most despicable of creatures in the earth and
air, were richer than he. This he said, to convince the Scribe of his
mistake; who expected much worldly grandeur and wealth, by becoming
his disciple.
As a matter of fact, Gills Exposition refutes he entire argument put forth by Yitzchak ben Avraham
When Christ styles himself "the son of man", it is no contradiction to
his being God; nor any objection to trust and confidence in him, as
the Jew (z) suggests; for he is truly and properly God, as well as
really man, having two natures, human and divine, united in his
person; so that he is, as was prophesied of him, Emmanuel, God with
us, in our nature, God manifested in the flesh: and since he is so, it
cannot be unlawful to trust in him; which it would be indeed, was he a
mere man. The Jews ought not to object to this name and title of the
"Messiah, the son of man": since he is so called, as their own writers
and commentators acknowledge, in (a) Psalm 80:17 and (b) Daniel 7:13.
And whereas it is further urged against these words of Christ, that if
he was God, why does he complain of want of place? Is not the whole
world his, according to Psalm 24:1? It may be replied, that it is very
true, that the whole world is his, nor could he be in want of
anything, as God; but yet, as man, for our sakes he became "poor",
that we "might be rich": nor should this be any difficulty with a Jew,
when they themselves say, as some have thought, if he (the Messiah)
should come, , "there's no place in which he can sit down" (c). Unless
it be understood of Nebuchadnezzar, as the gloss explains it; let the
learned inspect the place, and judge: the coming of the Messiah is
immediately spoken of.
As does Matthew Henry's Concise Commentary
8:18-22 One of the scribes was too hasty in promising; he proffers
himself to be a close follower of Christ. He seems to be very
resolute. Many resolutions for religion are produced by sudden
conviction, and taken up without due consideration; these come to
nothing. When this scribe offered to follow Christ, one would think he
should have been encouraged; one scribe might do more credit and
service than twelve fishermen; but Christ saw his heart, and answered
to its thoughts, and therein teaches all how to come to Christ. His
resolve seems to have been from a worldly, covetous principle; but
Christ had not a place to lay his head on, and if he follows him, he
must not expect to fare better than he fared. We have reason to think
this scribe went away. Another was too slow. Delay in doing is as bad
on the one hand, as hastiness in resolving is on the other. He asked
leave to attend his father to his grave, and then he would be at
Christ's service. This seemed reasonable, yet it was not right. He had
not true zeal for the work. Burying the dead, especially a dead
father, is a good work, but it is not thy work at this time. If Christ
requires our service, affection even for the nearest and dearest
relatives, and for things otherwise our duty, must give way. An
unwilling mind never wants an excuse. Jesus said to him, Follow me;
and, no doubt, power went with this word to him as to others; he did
follow Christ, and cleaved to him. The scribe said, I will follow
thee; to this man Christ said, Follow me; comparing them together, it
shows that we are brought to Christ by the force of his call to us, Ro
9:16.
The idea that Jesus "knew He wasn't God" doesn't hold water in light of other Scripture, either. It would be laughable if it weren't so sad. The question "Did Jesus claim to be God?" has been answered and addressed so thoroughly, and is such an established teaching, that it's simply ridiculous to try to claim otherwise. One example here.
The whole argument ignores the basic orthodox Christian teaching that Jesus assumed a humble nature willingly, for His purpose, but knew full well of His divinity.
