First, a clarification: When I say "Calvinist" I mean it only as a well-known label to quickly sum-up a system of beliefs commonly known as the Doctrines of Grace (DofG). I fully realize there are those who believe the DofG who take issue with being called "Calvinist" since it implies following after a man rather than what they believe are biblical doctrines. Fair enough, so know that I am using the term here in its more general sense as a label.
So, with that out of the way...
... a few years ago, in being challenged on my Calvinist beliefs I was confronted with the reality that, to cling to Calvinism, I would have to accept as true something called Pre-faith regeneration (PfR). Basically, this means that before someone can believe unto salvation they have to first (logically if not sequentially) be regenerated with new life by God to even be able to believe in the first place. This is logically demanded by Calvinism's view of fallen man's depravity which renders the Biblical order of salvation backwards and/or incomplete in many many verses.
There are many examples but here are just a couple to get started:
Bible view -- "... whoever believes in Him shall not perish, but have eternal life. "
PfR view -- "... whoever has life shall not perish but believes in Him"
Bible view -- "Truly, truly, I say to you, he who believes has eternal life"
PfR view -- "Truly, truly, I say to you, he who has eternal life believes in Him."
There are many many more examples, but you get the point -- If PfR is true it means the Holy Spirit essentially inspired these and many other verses regarding belief unto everlasting life... backwards! Rather, any natural reading of the Bible paints new life as clearly the result of belief, not the other way around as PfR demands. Since PfR is unbiblical yet required by Calvinism's view of depravity it became evident that strict Calvinism was askew. Not to say Calvinism is all bad, not at all (or second son does bear his name in-the-middle after-all), but if a premise leads to a clearly faulty conclusion then one ought reexamine the premise.
For further reading, please see the following:
Lordship's (out of order) Salvation
The Danger of Teaching that Regeneration Precedes Faith