Some verses have already been mentioned, and I'm heading out the door and have no time, but another is 2Pet3:9:
...He is patient with you, not wanting anyone to perish, but everyone to come to repentence.
Calvists have to either ignore that verse or else go through some extreme mental gymnastics to explain it away. However, it is in perfect harmony with the non-Calvist view, as well as the rest of Scripture, which teaches that God offers redemption to all through Jesus, and that most won't accept it. In addition to those who reject Christ outright, many will acknowledge Jesus as their Savior but aren't willing to serve Him as their Lord, i.e., they treat Him as sort of a spiritual genie in a bottle who is there to bail them out when things are tough.
So you are a universalist? If God wants EVERYONE to be saved and God is all powerful then under your view of the verse then everybody gets saved or God is not all powerful. You can't have it both ways.
Calvists have to either ignore [2 Peter 3:9] or else go through some extreme mental gymnastics to explain it away.
Wow. I didn't know that reading a passage in the context of its own paragraph was considered "extreme mental gymnastics". What do you call a hermeneutic that ignores all of the rules of context, forgets that one is reading a flawed paraphrased translation, and just jams in there an a priori meaning when it isn't justified?
Let me provide some clues.
2 Peter 1:1-2"To those who have received a faith of the same kind as ours, by the righteousness of our God and Savior, Jesus Christ...This is now, beloved, the second letter I am writing to you (3:1)... But do not let this one fact escape your notice, beloved (3:8)
Any guess to who the audience of this letter is? Now skipping past your choice in a flawed paraphrase, more faithful English translations say:
2 Peter 3:9 The Lord is not slack concerning His promise, as some count slackness, but is longsuffering toward us, not willing that any should perish but that all should come to repentance.
What promise is Peter referring to? Is this a promise made by God to everyone head-for-head? And if you foolishly claim that this promise to save is made to everyone, head-for-head, then you do indeed have a doctrine of universal salvation with only contradicting evidence for it. Furthermore, we have the word "us", and from a Calvinistic standpoint, the "us" is the audience to whom Peter writes this letter. Peter doesn't write this letter to the Reprobate because they couldn't understand it anyway and would consider it all foolish(1 Cor 2:14).
On the other hand, your mental gymnastics requires you to have a god that either contradicts Himself and provides universal salvation, or you have an impotent god that breaks his promises.
I actually love this passage because it tells us the exact conditions for when our LORD returns. Unlike the Dysfunctionalists who say that Israel has to do this, or the AntiChrist needs to do that, Peter simply tells us that our LORD will return when the last of the Elect is Redeemed.
Your doctrine teaches that God is an impotent failure who just happens to have good intentions but not the juice to pull it off. You can keep your doctrine, because it destroys all hope because salvation, in your scheme, is fully contingent on flawed and corrupted man with no help from God.