Your Muslim friend has it backwards. God did not become a man so that he  (God) would know what we are like (he already knew that–he made us) but so that we would know what he is like. The clayman does not need to become clay to know what is clay, but the clay will never know what the clayman is like unless the clayman becomes clay himself. This is the whole point of John 1:14. “The Word (that is, the eternal Son of God) became flesh and dwelt among us and we beheld his glory.” And John 1:18 says, “No one has ever seen God, but God the One and Only,who is at the Father’s side, has made him known.” The Muslim agrees with the first part of this–no one has ever seen God–but the Muslim religion leaves it right there.

Here we see the fundamental difference between Christianity and Islam. Islam posits a transcendent God, high and lifted up, far removed from us. Christianity says that God so loved the world that he not only cared for the world, he entered the world in the Person of the Lord Jesus Christ.

So the purpose of the Incarnation is for God to know,
It’s for us to know God.

See When Did Christmas Begin?