The reality of Christ's humanity is one of the most important points of Christian doctrine. Remember what St. John said: the one who denies that Christ is come in the flesh is Anti-Christ. Heresies about Christ's humanity have plagued the Church since the time of the Apostles: in one way or another, different people have sought to disconnect the Lord from our humanity. It is a grievous error.
The wonder of the Incarnation is that Christ fully assumed human nature. Mary truly is Theotokos, because God did not become human merely in semblance. He did not spurn having a human mother, from whom He truly inherited genetic material. He took on a fully human nature, perfectly and indivisibly united to His divinity, in one person. In so doing He broguht salvation to man, by turning the direction of man back to God. As a man, beset by our weaknesses, He overcame temptation and struck down sin and death. Becasue He was man He was able to assume the curse we had brought down upon oursevles: but when He did so He dealt an end to it. As a man He was able to die: but in so doing He destroyed death. As a man prone to weakness He could be tempted by the devil: but He conquered over him.
Mat 7:11 "If you then, being evil, know how to give good gifts to your children, how much more will your Father who is in heaven give what is good to those who ask Him!"
You assume a person inherits their genetic makeup from the mother. I would disagree and say the genetic makeup is from the father. In this sense the literal Father. After all the Nicene Creed itself states Christ was "conceived by the Holy Spirit".
Whether it is Mary's "egg" or God miraculously planted the whole thing is inconsequential. Sin is transmitted through the male and Mary was impreganted with perfection. One could possibly say all women eggs are pure and holy. It is the man who is the problem.