No, you're not getting the point of the argument. Paul isn't pointing out that God has predetermined people for wrath or mercy. Paul is simply pointing out a logical fact. If I know that my dog is going to dig a hole two minutes after he is tossed a bone, and that he will then bury it, this in no way denies that my dog is doing this of his own free will. I can't know this with 100% accuracy unless it is predestined. Here again, this doesn't negate the dog's free will. If I also know that two seconds before he is going to begin digging, a squirrel will dart out from the side of his dog house, I know that he will not commence digging, but will instead give chase to the squirrel instead. Here again, no one is being denied their free will. This doesn't negate the fact that God is omniscient, and God's omniscience cannot be relied upon if any number of factors are unknown. It is to contradict the meaning of omniscience.
God insures that his will is carried out. It is only our assumptions that free will cannot exist along side predestination that causes confusion.
Again, you can't fly to the moon. You weren't designed to fly at all, but this doesn't impinge upon the fact that you still have free will. It is the same with Paul's argument. The carnal mind is emnity against God, and can never please God. Does this mean that the carnal mind has no free will? Nope. It just means that it is useless for attaining salvation.
God's promises are by faith, "and that not of yourselves". It's not your or my faith that saves anyone. It's completely out of our hands as far as the will of the carnal mind goes.
The bible points out that "the whole world is deceived", and deceived people cannot choose to do the right thing for the right reasons.
This is something I've pointed out in other threads in the past that we are deluded if we think that there is anything we can do to sustain ourselves. It is only by the providence of God that anyone is able to do anything in the first place. Christ points out that apart from him we can do nothing. Yet we continue to work for Mammon rather than for God. Our actions betray our so-called beliefs, and spotlight that we can only make feeble attempts to believe what we have no ability to see.
Thus it must be by revelation from God that anyone can begin to see the truth, and THEN believe. The bible is the testimony of witnesses, not those who just believe what they've been told.