“Because I was given the statement that the non-elect can ONLY choose to sin.”
Why do you think there is any contradiction between “only choose to sin” and doing good?
Jesus says unless our righteousness exceeds that of the pharisees we cannot enter the kingdom of God. Paul says in 1 Cor. 13:3, “And though I bestow all my goods to feed the poor, and though I give my body to be burned, and have not charity, it profiteth me nothing.” That is not a treacly sentimental affection but a lovining response to God who loved us first. So how can an unbeliever love like that when he has not experienced the love of God? He can do good but always for the wrong motives because he has no relationship with the One who is good..
Because sin is bad?
Amen.