Amen! Although it is our responsibility to choose to believe and we will be held accountable for unbelief (John 3:18), saving faith in Christ is never exclusively a matter of human decision. Unless the Father draws us (John 6:44) and enables us/it has been granted from the Father (John 6:65), we would NEVER come to believe/place saving faith in Christ all by ourselves. The approach of the soul to Christ is initiated by the Father, but He doesn't force us to choose Christ, we must choose Him. The impulse to faith in Christ comes from God.
My friend, you have just given the perfect depiction of prevenient grace. However, what you have posted, in my opinion, is wrong.
Please allow me to elaborate. The word used for draw is in John 6:44 is helko(pronounced hel-Koo-o), and it means to lead, impel, to literally drag off. It is used in John 18:10 when Peter drew his sword, and in John 21:11 when Peter drew the net to shore. It’s also found in Acts of the Apostles 16:19 when they drew Paul and Silas into the marketplace. Also in Acts of the Apostles 21:30 when they drew Peter out of the temple. In each instance, it denotes an effectual drawing, which is what literally to drag off means. Not that He draws us kicking and screaming, but that He effectually draws us to Himself. He draws, we come, it’s just that simple.
Now, you said it is up to us to choose, so you put the onus of salvation upon man’s ability, or inability, to choose Him. God draws, but man must choose to come, or not. In no way does helko promote that idea. If God is drawing two mean equally, if one chooses to come, they’re saved. If the other chooses not to, he won’t be saved. The reason why the one isn’t saved, is not because God didn’t try to draw him, but it was his refusal to come. So it was the one who chose to come who is saved, because he chose to come. The onus of his salvation wasn’t based on God’s drawing him, because the other guy was equally drawn but refused, but because he chose to do what the other didn’t.
Plus, God doesn’t just call, but hunts His sheep down, picks them up and puts them into the sheep pen. Please read Matthew 18:12-14, with careful attention to the last sentence and compare that to 2 Peter 3:9.
“What do you think? If any man has a hundred sheep, and one of them has gone astray, does he not leave the ninety-nine on the mountains and go and search for the one that is straying? If it turns out that he finds it, truly I say to you, he rejoices over it more than over the ninety-nine which have not gone astray. So it is not the will of your Father who is in heaven that one of these little ones perish.[Matthew 18:12-14]
The Lord is not slow about His promise, as some count slowness, but is patient toward you, not wishing for any to perish but for all to come to repentance.[2 Peter 3:9]
In both places, it speaks to the fact God is not willing any of His sheep perish. Much so, that He hunts them down, quickens them, gives them the gifts of faith and repentance, and they are saved.
I pray you consider this post with some deep prayer and study.
Thank you for reading this post, my Brother.