Before properly rejecting it as obviously untrue, let's follow the philosophical path taken by most of those who say "Calvinism kills evangelism" and consider the merits of my assertion. Just like Calvinists, Arminians believe that God wants to save everybody in some sense, but that there is another consideration that overrides His acting on that desire and saving everybody. Calvinists would say that consideration is His glory, which can only be fully displayed in both His wrath and His mercy. It is my understanding that Arminians, on the other hand, generally believe that consideration is God's respect of our free will. (At least, that's what I would have said when I was among their honorable ranks.) C. S. Lewis said that God did not want to create an army of puppets; that, to quote the Free Will Song, "only willing love is worth the price." Thus, God cannot save everybody, though He wants to, because He wants more to respect our free will. That's His higher will that overrides His will that all be saved, just as Calvinists say that God's higher will that His glory be increased overrides His will that all be saved.
Let's see how the Arminian understanding plays out in the question of whether we should pray for our unsaved friends and relatives. First, logically, it means that we can't make a request of God to override the person's free will; we can't say "Lord, change his/her heart," because that would be against what we understand his will to be. We know that "praying in Jesus's name" cannot mean praying for something that we know is against His will; thus, following the idea that God's highest will is to respect our free will, we can't pray for God to save somebody.
I should note that some people may object that prayer is not simply making supplication; there are other sorts of prayer that are simply "communing" with God, thanking God, praising Him, etc. I would certainly agree with that, but I don't think that's what people actually do when they are praying for somebody else's salvation. I don't think they simply say "O God, thank you for your greatness in saving me and for your greatness in respecting X's free will." That's a valid prayer (and perhaps the kind worth praying more often), but it is not praying for the other person's salvation, so I don't think that's the way most pray. Certainly, that's not what they've done in my presence.
So, the best we can pray for given that understanding of God's will - and this is what I often tried to do when I was an Arminian myself - is that God will do His will in the situation, whatever that may be. That, too, seems unsatisfying. We have such a love for our unsaved family and friends, such a desire to see them saved by God as we know that we have been saved by Him - for who among us would have the temerity to boast that it was thanks to our own free choice that we accepted God's saving grace? - that we cannot help wanting to pray for the person's salvation. Sure, we want God's will in every situation; but, like David in many Psalms, cannot help crying out our desire for God's intervention. So, how can we pray?
What if we pray for God to change the circumstances of the person's life so that he will accept the Gospel? Surely we can pray for God to change those, so the person will then accept God of his own free will. At least, that's the kind of conclusion that I drew when I was an Arminian myself, and often prayed that way. However, let's consider that answer in the full light of our libertarian free will assumption. It seems like the circumstances around the person that God might change might be of two types: the people around him, and the inanimate objects and situations around him. Let's consider each in turn.
- If the circumstances that need changing are other people around him, them what about their free will? If God so respects free will, He needs to respect their free will also. Does God only respect the free will of people He foresees as coming to faith in him in faith and thus making themselves part of the elect? And what verse does that come from?
- On the other hand, if the circumstances only include purely inanimate objects, isn't God bribing the person? Isn't this like saying either "you are free to love me or not; ignore this million dollars I'm holding in front of you" or "you are free to love me or not, pay no attention to the gun I'm holding to your head"? Either way, positively or negatively, God is coercing the person's will; and if "only willing love is worth the price," that kind of coerced love is not "willing" in any important sense I can think of.
However, unlike some who take a misunderstood understanding of unconditional election and assume that therefore Calvinists don't evangelize, I do not reach the conclusion that actual Arminians don't pray for their friends' and family's salvation. To their credit, most Arminians do not follow their philosophy to this logical end. They pray for their friends and loved ones with fervor, asking God to change their hearts. I have heard it myself; I prayed it myself (thought not as sincerely, no doubt, as many) when I was in more or less the same state of mind and emotions.
So, what is my point? Just the same as my other Outrageously Untrue Assertions: that you cannot take a understanding of somebody's philosophy and assume that they act on that philosophy the way you think they will. And that for two reasons:
- First, they may not act consistently with their philosophy: it was C. S. Lewis who said that he would rather play cards with a man who had doubts about ultimate questions of right and wrong but who had been raised with the understanding that "gentlemen do not cheat" than with an impeccable moral philosopher who had been raised by card sharps. People often don't act consistently with their philosophy, and I am extremely grateful for that. Otherwise atheists would be following their assumed "law of the survival of the fittest," whose primary duty - if one is to improve the human race's condition - would have to be to ruthlessly conquer everything in sight. In other words, even if it were true that Calvinism per se discouraged evangelism - which I am far from granting - you cannot assume that any given Calvinist will disdain evangelism themselves.
- Second, your understanding of that philosophy may be faulty. My understanding of Arminian philosophy may be faulty, I don't know; one is perhaps a poor judge of one's own positions on things. However, I can say for sure that the vast majority of Arminians I have talked to and listened to misunderstand Calvinist theology. Many hear things that don't exist ("The doctrine of Unconditional Election means there's no reason to evangelize") and ignore things that do ("What do you mean God wants all to be saved? So why doesn't He save them?")