No, they don't come, so they are not rejected.
You say they are rejected because they don't come, but your system teaches that they can't come unless enabled and that God chose before the foundation of the world which ones he would enable and which ones he would not. So, in your system, they are don't come because they were rejected (not enabled).
the problem is that your objection is faulty. You have a system that is somehow obligated to offer salvation to all, which just simply isn't true
Untrue. As I've said many times before, "The wonder of God's mercy and grace is NOT that He doesn't save everyone; it is that He even saves ANYONE!"
This is the very essence of what I believe, even as a non-Calvinist. God is not in any way morally obligated to save anyone because we deserve it. Again, this is a point upon which we can all agree.
However,
God has obligated Himself, both morally and judicially, to save whosoever will come (believe). Not because they deserve it, but because He sent forth His Son to be a propitiation for sins of whole world, which is to be applied only through faith. His universal call to "every creature" to faith and repentance obligates him to save whosoever repents and believes. The doctrine that teaches that God only grants this ability to willingly repent and believe to a select few while appearing to call "every creature" is what causes the non-Calvinists to cry, "Foul!"
I don't believe the Calvinistic view of God is unjust because he condemns certain people to hell. I believe the Calvinistic view of God is unjust because He offers a pardon to all mankind while only granted a few of them the ability to receive it, all the while expressing a desire for all to come to repentance and a frustration for those who remain unwilling.
It is deceptive to offer someone a gift you fully know they cannot willingly receive. Especially if you, the giver, are the one who determines the receivers natural abilities. That type of offer cannot be geniune!
I find it so interesting that the non-cals think they know more about our theology than we do.
Which form of "your theology" are you referring to?
As I've quoted before,
Calvinists are seriously divided among themselves and always have been. There is Supralapsarianism vs. Sublapsarianism vs. Infralapsarianism. 'The Supralapsarians hold that God decreed the fall of Adam; the Sublapsarians, that he permitted it' (McClintock & Strong). The Calvinists at the Synod of Dort were divided on many issues, including lapsarianism. The Swiss Calvinists who wrote the Helvetic Consensus Formula in 1675 were in conflict with the French Calvinists of the School of Saumur. There are Strict Calvinists and Moderate Calvinists, Hyper and non-Hyper (differing especially on reprobation and the extent of the atonement and whether God loves all men), 5 pointers, 4 pointers, 3 pointers, 2 pointers. In America Calvinists were divided into Old School and the New School. As we have seen, the Calvinists of England were divided in the 19th century.
Whenever, therefore, one tries to state TULIP theology and then refute it, there are Calvinists who will argue with you that you are misrepresenting Calvinism. It is not so much that you are misrepresenting Calvinism, though. You might be quoting directly from various Calvinists or even from Calvin himself. The problem is that you are misrepresenting THEIR Calvinism! There are Calvin Calvinists and Thomas Fuller Calvinists and Arthur W. Pink Calvinists and Presbyterian Calvinists and Baptist Calvinists and many other sorts of Calvinists. Many Calvinists have never read Calvin’s Institutes of Christian Religion for themselves. They are merely following someone who follows someone who allegedly follows Calvin (who, by his own admission, followed Augustine)."
Calvinists believe that they have the right to reject or modify some parts of or conclusions of Calvin. I agree with them 100%, and I say, further, that we also have the right to reject the entire thing if we are convinced that it is not supported by Scripture!