There is so much wrong with that, I don't know where to begin.
John 1:12 But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name:
13 Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God.
If you are correct, and God first regerates a man to receive Christ (which is explained further as believeing on him), then you are teaching that a man who has already been made alive by Christ needs to be born again.
Why would somebody who is already spirtually alive need to receive Christ? Why would God have to give them the power to become the sons of God if they are already born of God?
13 who were born, not of blood [not of superior human descent such as the Jews believed], nor of the will of the flesh [not because of the individual's choice], nor of the will of man [not because someone persuaded the individual], but of God.
You got part of that right. No one is saved through the blood. John the Baptist showed that no one was saved because they were the physical descendent of Abraham.
Matt 3:7 But when he saw many of the Pharisees and Sadducees come to his baptism, he said unto them, O generation of vipers, who hath warned you to flee from the wrath to come?
8 Bring forth therefore fruits meet for repentance:
9 And think not to say within yourselves, We have Abraham to our father: for I say unto you, that God is able of these stones to raise up children unto Abraham.
But when verse 13 says we were not born of the will of the flesh, or the will of man, it is not saying that man's will is not involved in salvation. It is saying that the Gospel, the method that God has chosen to save man was wholly God's idea and plan and man played no part in it.
And very experience shows this. Look at all the religions in the world, what do they teach? Except for true Christianity they all teach that a man can earn his way to heaven by his own efforts.
There are really only two religions in the world, those who trust in Christ, and those who trust in their own goodness or works.
Man, if left to himself to devise a method of salvation will ALWAYS without fail choose works. And the history of religion proves this.
Rom 9:31 But Israel, which followed after the law of righteousness, hath not attained to the law of righteousness.
32 Wherefore? Because they sought it not by faith, but as it were by the works of the law. For they stumbled at that stumblingstone;
Rom 10:1 Brethren, my heart's desire and prayer to God for Israel is, that they might be saved.
2 For I bear them record that
they have a zeal of God, but not according to knowledge.
3 For they being ignorant of God's righteousness, and going about to establish their own righteousness, have not submitted themselves unto the righteousness of God.
So, give man his way and he will always choose works. Even some who call themselves Christian feel they have to add works to God's simple plan of salvation. They will say you have to be baptized to be saved, or go to church on Saturday, or keep the law.
This is the most difficult part of salvation, getting a man to trust Jesus Christ alone. Some call those who preach that a person only need believe on Christ to be saved of "easy believeism". They say it is easy, but it is not easy for them, they always have to add something extra to the Gospel.
Without God's word, neither you, nor I, nor anyone else would ever dream up the idea of God himself coming to the world and being born in the flesh under the law, going to the cross bearing our sins, and rising from the dead.
So the Gospel, the plan and method of salvation is 100% God's idea and 100% of his will alone. That is what verse 13 is saying.
Isa 64:4 For since the beginning of the world men have not heard, nor perceived by the ear, neither hath the eye seen, O God, beside thee, what he hath prepared for him that waiteth for him.
1 Cor 2:9 But as it is written, Eye hath not seen, nor ear heard, neither have entered into the heart of man, the things which God hath prepared for them that love him.