First off all, I would like to say, do not mention the word "logical" when discussing the nature of God. You Muslims say the Father, Son, and Holy Spirit being God is illogical because it is mathematically impossible, yet you Muslims believe in the virgin birth which is biologically impossible. So please, logic plays no key in this debate.
Secondly, I agree with you that when Christ says He and the Father are one, that does not necessarily mean that Jesus is God. But the passages which display oneness do not need to be used to show that Christ is God. There are way better passages:
Phillippians 2:5-8>Let this mind be in you, which was also in Christ Jesus: Who, being in the form of God, thought it not robbery to be equal with God: But made himself of no reputation, and took upon him the form of a servant, and was made in the likeness of men: And being found in fashion as a man, he humbled himself, and became obedient unto death, even the death of the cross.
Jesus is God in the flesh:
1 Timothy 3:16>And without controversy great is the mystery of godliness: God was manifest in the flesh, justified in the Spirit, seen of angels, preached unto the Gentiles, believed on in the world, received up into glory.
Colossians 1:14-15>In whom (Jesus) we have redemption through His blood, even the forgiveness of sins: Who is the image of the invisible God, the firstborn {Inheritor} of every creature:
Colossians 2:9-10>For in Him (Jesus) dwelleth all the fulness of the Godhead bodily. And ye are complete in Him, which is the head of all principality and power:
Hebrews 1:8>But unto the Son (Jesus) He (Father) saith, Thy throne, O God, is forever and ever: a scepter of righteousness is the scepter of thy Kingdom.
Mark 2:5-12>When Jesus saw their faith, He said unto the sick of the palsy, Son, thy sins be forgiven thee. But there were certain of the scribes sitting there, and reasoning in their hearts, Why doth this man thus speak blasphemies? who can forgive sins but God only? But that ye may know that the Son of man hath power on earth to forgive sins, He saith to the sick of the palsy, I say unto thee, Arise, and take up thy bed, and go thy way into thine house. And immediately he arose, took up the bed, and went forth before them all; insomuch that they were all amazed, and glorified God, saying, We never saw it on this fashion.
etc, etc, etc.
So as you see here, by using the Holy Bible, your claim that Christ is not God because of His human qualities is refuted. Not only that, but several more passages are given to support the notion that Christ is God in the flesh. Finally, the "etc, etc, etc" I have at the bottom indicates that there are plenty more passages which support the truth that Christ is God incarnate.