Christians as well as Jews believe that God made the Israelites as his "Chosen People."
Why does God need a Chosen People at all?
The Scripture isn't clear on why, but here are a few suggestions that make sense to me.
God made a lot of choices throughout history and it helps to understand the broader perspective.
The First Man and Woman
He created Adam and Eve 1) in His image, 2) to populate the earth. The results were to be a world full of people in the image of God, worshiping Him, exercising dominion, ruling and bringing things to fruitfulness.
However, Adam and Eve fell, so the image of God in them was now marred to some extent. This culminated at the time of Noah when God was grieved with the evil in the world and that "every inclination of the thoughts of men were only evil all the time." Even though the population had increased significantly and was filling the earth, it was with the wrong kind of people--evil people. God indicates in the judgment of Adam and Eve that an ultimate solution will one day come--the Seed of the woman.
The Man of Favor
Then, Noah chose Noah--a righteous man, blameless among the people of his day. That is the kind of people God wanted to populate the earth. So, God judged the wickedness and started over with Noah, the man of favor.
This failed at Babel when the people refused to be "scattered over the face of the earth", which is specifically what God had commanded. So, God confused their languages to force them to fulfill His command. This fulfilled one part of His divine plan--people were scattering over the earth, but they were people who had to be forced to do so because of their rebellion. So, in order to have a world full of people in the image of God with whom God could enjoy relations, God had to have a plan to reach all people all over the world.
The Man of Faith
Enter Abraham. Although it took many years for Abraham to develop into the man of faith, that was precisely God's plan--that Abraham and his descendants (the chosen people) would ultimately be a blessing to all people (who were now scattered over the whole face of the earth).
Israel also failed to do this fully, although there were considerable successes. Through the Exodus, the Egyptians would know that there was a God in Israel as God answered Pharaoh's question, "Who is the Lord?" Through Daniel, Nebuchadnezzar recognized the God of Israel and even wrote a letter to his entire kingdom proclaiming the greatness of God Most High. Many other examples could be cited. However, ultimately Israel continued to reject God again and again and failed to be His messengers to the whole world. The House of Prayer for all nations became a place restricted to Israelites only, and Jesus Himself cleared the court of the Gentiles that was being used as a market rather than a place for the Gentiles to worship.
Still, in the lineage of Jesus, mention is made of several Gentiles who worshiped the God of Israel (and the world), including Rahab of Jericho and Ruth of Moab. Even Bathsheeba was the wife of Urriah the Hittite.
God's ultimate plan, mentioned in the curse of Adam and the blessing of Abraham (as well as many other places) culminated in the Messiah, as God the Son entered the world through the Virgin Birth, paid the penalty for sins so that men could be forgiven and be indwelt by the Holy Spirit. This would enable men to live more righteously through the power of God.
Jesus final words were a commission to the disciples (now apostles--ones sent out with a message). Their task--to take the gospel to "all the nations of the earth", so that all men may know the one true God and live righteously in relationship with Him.
The Church--now the "chosen people" of God based on faith rather than ethnicity--has certainly had its own share of failures. However, according to Wycliffe, the Word of God will become available to all the languages of the world probably by the end of this century.
The gospel will indeed soon reach all people of the earth. This was the commission to 11 common, ordinary men who dealt with extreme persecution by their own people as well as the Romans. It was quite a bold prediction that one day people from "every tribe, language and people" would recognize Jesus as Messiah in those early days (Revelation 5:9; 7:9). Yet, that is a very probably reality within the next 50-100 years.
So, God chose the people of Israel for a time (about 2000 years) to fulfill His ultimate purpose for all time. Israel succeeded in part, but the ultimate plan was for them to be the people from whom the Messiah would come. The Church was born by the people of Israel. Even now, many Jewish people are recognizing Jesus as their Messiah.
From a Jehovah's Witness perspective
As the ALMIGHTY Sovereign Lord and Creator of all Heaven & Earth, the physical and spiritual universe and everything within, Almighty JEHOVAH God doesn't "need" anything at all being that he is quite literally complete within himself.
Jehovah God has a "chosen people" due to the Holy covenant / agreement he long ago made with Abraham because of Abraham's tremendous act of faith and love shown to God on account of Abraham's only begotten son Isaac. This Holy covenant / agreement extended to Abraham's decendants (Isaac, Isaac's son Jacob whom God renamed Israel, to Jacob's / Israel's children who became known as Israelites).
JEHOVAH loved Abraham, so He showed loyal love to Abraham’s descendants. For over 15 centuries, he viewed the nation of Israel, which descended from Abraham, as his chosen people, his “special property.” (Read Deuteronomy 7:6.) Did that mean that Jehovah totally disregarded people of other nations? No. During that time, non-Israelites who desired to worship Jehovah God were allowed to attach themselves to his special nation. These converts, or proselytes, were viewed as part of the nation. They were to be treated as brothers. (Lev. 19:33, 34) And they were required to obey all of Jehovah’s laws.—Lev. 24:22.
However, Jesus Christ (the only begotten Son of Almighty Jehovah God) made this startling declaration to the Jews of his day: “The kingdom of God will be taken from you and be given to a nation producing its fruits.” (Matt. 21:43) Who would make up this new nation, and how are we today affected by this change?
The apostle Peter clearly identified this new nation. He wrote the following to his fellow Christians: “You are ‘a chosen race, a royal priesthood, a holy nation, a people for special possession, that you should declare abroad the excellencies’ of the one that called you out of darkness into his wonderful light.” (1 Pet. 2:9) As foretold, natural Jews who accepted Jesus as the Messiah were the first members of that new nation. (Dan. 9:27a; Matt. 10:6) Later, many non-Israelites were also included in this nation, for Peter went on to say: “You were once not a people, but are now God’s people.”—1 Pet. 2:10.
To whom was Peter here speaking? In the beginning of his letter, he says: “[God] gave us a new birth to a living hope through the resurrection of Jesus Christ from the dead, to an incorruptible and undefiled and unfading inheritance. It is reserved in the heavens for you.” (1 Pet. 1:3, 4) So this new nation is made up of anointed Christians, who have the heavenly hope. They are “the Israel of God.” mentioned at Galatians 6:16. In a vision, the apostle John saw that these Spiritual Israelites number 144,000. They are “bought from among mankind as firstfruits to God and to the Lamb” to serve as “priests” and to “rule as kings with [Jesus] for the thousand years.”—Rev. 5:10; 7:4; 14:1, 4; 20:6; Jas. 1:18.
Clearly, then, the phrase “Israel of God” at Galatians 6:16 refers exclusively to anointed Christians. However, are there instances when Jehovah uses the nation of Israel as a picture, or illustration, that includes Christians other than the anointed who have the God given hope of ruling alongside Christ as kings / priests in the Heavenly Kingdom? The answer can be found in these words of Jesus to his faithful apostles: “I make a covenant with you, just as my Father has made a covenant with me, for a kingdom, that you may eat and drink at my table in my kingdom, and sit on thrones to judge the twelve tribes of Israel.” (Luke 22:28-30) This will take place during “the re-creation,” or time of regeneration, during Christ’s foretold Millennial Rule.—Read Matthew 19:28
The 144,000 will serve as heavenly kings, priests, and judges during the Thousand Year Reign. (Rev. 20:4) Whom will they judge, and over whom will they rule? At Matthew 19:28 and Luke 22:30, we are told that they will judge “the twelve tribes of Israel.” Whom do “the twelve tribes of Israel” picture in this context? They represent all those with an earthly hope who will be ruled over as royal subjects of the Heavenly Kingdom. They put faith in Jesus’ ransom sacrifice but *are not included in the royal ruling priestly class*. (The tribe of Levi was not included in the listing of the 12 tribes of natural Israel.) Those pictured in this context by the 12 tribes of Israel are the ones who will gain spiritual benefits from the priestly services of the 144,000. They are the ones whom Jesus' words at Matthew 5:5 apply being that such ones are comprised of "the meek" who will inherit, not heaven, but rather... The Earth (when the Earth is transformed to the paradisaic state it was meant to be acording to God's purpose. These nonpriestly beneficiaries are also God’s people, and he loves and accepts them. It is appropriate that they are likened to his people of ancient times.
There is a biblical explanation for God's chosen people in the Book of Deuteronomy, especially if we go back to the earliest manuscript versions of Deuteronomy 32:8-9, available to us in earlier Septuagint and Dead Sea texts. Paul Sanders (Provenance of Deuteronomy Thirty-two, pages 154-160) says scholars now generally assume that the traditional Masoretic Text is the result of adaptation of the older reading for theological reasons.
Deuteronomy tells us that each of the gods received a nation as his portion. Yahweh received Jacob, or Israel, as his portion: his chosen people.
First, the MT says, along with most Christian Bibles:
Deuteronomy 32:8-9: When the most High divided to the nations their inheritance, when he separated the sons of Adam, he set the bounds of the people according to the number of the children of Israel. For the LORD'S portion is his people; Jacob is the lot of his inheritance. (KJV)
Some earlier LXX manuscripts, supported by the two Qumran texts, say "according to the sons of God":
Deuteronomy 32:8-9: When the Most High gave the nations as possessions, when he separated the sons of man, he established the areas of the peoples according to the number of the sons of God. However the portion of Yahweh is his people; Jacob is his inherited share. (Provenance of Deuteronomy Thirty-two)
According to what appears to be the earliest reading of Deuteronomy 32:8-9, the Most High God gave Yahweh God the Israelites as his chosen people.