"so Christ also, having been offered once to bear the sins of many, will appear a second time, without sin, to those who are eagerly waiting for him for salvation" Hebrews 9:28

The flesh is not able and does not want to submit to God. It has a Will but that will is enslaved to sin ad Paul so frequently makes clear.

The point being Jesus does not say you are not my sheep because you have chosen not to believe but says you do no believe because you are not my sheep. Therefore, using basic logic, if one is of Christ's sheep they will believe. If not, then they will remain just as blind as the Pharisees for without the Spirit of God one cannot discern spiritual truths (1 Corinthians 2:14) God picks his elect just as it is the shepherd that chooses his sheep, not the other way around.

He then continues to explain to the Pharisees the reason for their unbelief. Notice His surprising explanation.
*[[John 10:25-27 Jesus answered them, “I told you, and you do not believe. The works that I do in my Father’s name, these testify about me. But you do not believe, because you are not of my sheep. My sheep hear my voice, and I know them, and they follow me.

Why does the adulterous man hide his evil affair? No one wants to get caught and suffer the consequences. That's what that particular Scripture is teaching. The point of Romans 1 however, is that every man is without excuse and will be punished for their rejection and hatred of the God they know exists. This was our same state until God saved us. No man seeks God! No man understands! (Romans 3:11)

Rom 3:10-12 As it is written, “There is no one righteous; no, not one. There is no one who understands. There is no one who seeks after God. They have all turned aside. They have together become unprofitable. There is no one who does good, there is not even one.”
You are assuming something about yourself different from the rest of the sinful human race and the fact is none would seek God if He had not first transformed or wicked hearts. Praise be to His great name!

It is only those given to Christ by the Father that will be raised up on the lady day. No other group is involved.

Calvinism teaches that those who are truly saved will be sanctified and anyone claiming to be in Christ but walking in darkness is a liar. 1 John 1:6

This is called creating straw men. You are completely misrepresenting Calvinism. In reality What you are rejecting are your own false assumptions about Calvinism.