So we both believe sin is inevitable with fallen man. Therefore, your "logical conclusion" argument applies to both of us (in actuality, it applies to neither of us). God rigged the game, after all, so He is responsible. He put the tree in the garden, He lets Satan run wild. And all of that guarantees that sin and rebellion will flourish. We agree on all those things, so we are in the same boat with your logical conclusions.
However, you keep defining sin in terms of outward actions. And I stated above that T.D. does not teach that men will sin 100% of the time or be is bad as they could be. But let's look at sins of the heart. In fact, let's look at what Jesus said was the foremost commandment - love Lord God with all your heart, mind, soul and strength. I assume you would agree to break this commandment is a sin. Does the natural man have the "ability to do otherwise" and obey this commandment at all times?
Well, I disagree with you both. I believe man was created "flesh" and still is. The flesh naturally has desires. These desires are not necessarily evil, in fact they are necessary and helpful. Having an appetite is a good thing, we all need to eat for nourishment and good health. But if we do not control or keep in check our appetite, then we can become overweight and have health problems. It is the same with the natural affection men have for women. It is not wrong for a man to enjoy the physical beauty of his wife, but if a man looks on other women this way it is a sin.
God gave man freedom, but true freedom requires responsibility. If a man were to give himself over wholly to freedom, he is then enslaved by his passions. Freedom requires choice, so even with our natural desires a man must be able to say "no" to them, else he has no freedom.
If you read the account of Eve, it was not only the lie of Satan that tempted her, it was also her natural God-given desires.
Gen 3:6 And when the woman saw that the tree was good for food, and that it was pleasant to the eyes, and a tree to be desired to make one wise, she took of the fruit thereof, and did eat, and gave also unto her husband with her; and he did eat.
Adam and Eve were created "very good". They were sinless, pure, and upright. But they were "flesh" and so had natural desires. God gave them responsibility in that he gave them one command that they could not eat of the tree of knowledge of good and evil. Now they had true freedom, they had the choice of obeying or disobeying God. Without this command there could have been no responsibility, no restraint to their natural desires and so they would have been slaves to their desires.
There is only one change in man's nature shown after Adam and Eve sinned, and this is that they now knew both good and evil. But this is not evil, for God himself possesses this ability.
Gen 3:22 And the LORD God said, Behold, the man is become as one of us, to know good and evil: and now, lest he put forth his hand, and take also of the tree of life, and eat, and live for ever:
God did not create man evil, nor does he ever cause or tempt any man to do evil. But necessarily he must give man freedom to choose between right and wrong, else man could not love God. Love requires choice, it cannot be forced or imposed.
God did know in his foreknowledge that man would sin, but foreknowledge is not the same as determination as some falsely teach. We put up speed limit signs along the highway because we know beforehand that men will drive as fast as they possibly can, but knowing this does not cause them to drive over the limit.