As with all unbiblical doctrines, Calvinism can only be sustained by either ignoring or editing scripture. By far the most unbiblical aspect of Calvinism is Limited Atonement, for which there is quite literally no Biblical support. There is no verse, passage, or combination of textual extracts to which one could appeal to prove Limited Atonement. This is to the extent where if you find a 4 point Calvinist, you can be fairly certain Limited Atonement is the point they reject.
Aside from having no Biblical support, Limited Atonement is flat out disproven by many scriptures. Most notable among these is 1 Timothy 2:1-4, which tells us we should pray for all people, because God wants all people to be saved and come to the knowledge of the truth. This, of course, fits in very nicely with verses like Ezekiel 18:32, Ezekiel 33:11, John 3:16, 2 Peter 3:9, and 1 John 2:2, all of which say some variation of God not wanting to kill the wicked, but to save them, and thus the cross atones for their sins.
But Calvinists think they have the answer: change the scripture! Rather than letting it say "all men", as it does, they change it to say "all kinds of men". This is nowhere justified in the immediate context, nowhere justified elsewhere in scripture, and to this day, I can find no translation that agrees with this change. The text so clearly says God wants all men, not "all kinds" of men, that the only possible reason to want to change it to "all kinds of men" is specifically to fit Calvinism.
This is a process known as "eisegesis". That is, rather than starting with the text and using it to inform our beliefs, we start with our beliefs and force them into the text. Such a practice is usually reserved for heretics, apostates, and unbelievers. Nevertheless, in this case, Calvinists do it quite frequently. After all, "all" does not always mean "all", does it?
Let's take that logic. First, consider that God's desire for all men to be saved is Paul's justification for the command to pray for all men. No exceptions are given, no indication is given that this only applies to some men (plus that word "all" is a dead giveaway that there aren't supposed to be exceptions). How, then, are we to determine who we're supposed to pray for?
The word "all" is also found elsewhere in scripture. In Romans 3:23, all have sinned and fallen short of the glory of God. Well, maybe not all? Maybe this only refers to all kinds, but in each kind, there are innocents? 2 Timothy 3:16: all scripture is given by inspiration of God. Perhaps this means all kinds of scripture, so God might not have inspired Luke, but maybe He did inspire chapter 9 of the Qur'an? Acts 17:30, God commands all men everywhere to repent. Perhaps He's totally cool if the Russians stay in their sins? Maybe, in Genesis 6:22, Noah didn't actually do all God commanded? Perhaps that's where the dinosaurs went. God commanded him to take 2 of each kind, but Noah didn't like them, so he didn't take them.
Do you see the folly of changing scripture just to suit a certain theology? Calvinism may well be near and dear to the hearts of its adherents, but it cannot be sustained in light of what scripture actually says. A good Bible student will open his ears when the Holy Spirit speaks. The Lord guided the pens of His prophets and Apostles, of which John Calvin was neither. We are to judge him by their writings, not change their writings by his teachings. Through Paul, God tells us He wants all men to be saved and come to the knowledge of the truth. Therefore, let us make prayers, supplications, intercessions, and thanks for all men, just as He commanded.