I don’t pretend to speak for Gamecock, because he has the Scriptural picture well in hand and can defend himself, but I really don’t think he is saying that he considers himself more righteous than “that Arminian over there.”
On the contrary, he is saying he is not more deserving than anyone. Being elected for no reason visible to man makes this a very humbling proposition to anyone who comes to Christ. And, I am out on a limb here, but I certainly do not think that Arminians are necessarily not believers. If God elects, He can rescue anyone. But, we do know that a lot of rescued men and women believe mistakes about the Gospel and about what the Scripture teaches. Further, some believers teach error, and are still believers. Doesn’t mean we should encourage it, but errors have been part of our problem for all of history. Paul confronted Peter about his error of retreating from the Gentiles when the Judaizers showed up. Read Galations 2:7ff and watch the sparks fly. Peter was clearly in error and perhaps teaching some error, but Paul said he was sent to the Jews with the Gospel.
So, clarifying a mistaken understanding and accusing another of not being a believer are two different things. Your words indicate you have been captured by the great Hound of Heaven. He sought you, made you alive from the dead, clothed you in His righteousness. Why must this be initiated by you to be good news?
"...Paul confronted Peter about his error of retreating from the Gentiles when the Judaizers showed up...."
What is a 'Judaizer'? A 'God-Fearer' one who sympathized, with and practiced as far as possible, the Law of Moses, yet, not having been born in any of the twelve tribes, remained an gentile nevertheless? And when Peter retreated from his stance re: these gentiles was not at the insistence of James and his followers who grudgingly admitted the validity of the God-Fearers, but only as auxiliary to, not bona fide members of God's chosen people?
"...Paul said he was sent to the Jews with the Gospel..."
By 'gospel' do you mean Paul was sent 'to the Jews' to proclaim the fulfillment of Daniel's prophecy? To all the Jews?