I think I was predisposed to Calvinistic theology and against Arminian theology growing up. My dad (who doubled as my pastor) wouldn't have identified himself as Reformed or Calvinistic, but he strongly emphasized the doctrine of eternal security. I began to see, in seminary, how they ‘doctrines’ of grace all hang together – it’s really hard to consistently hold a doctrine of eternal security without also predestination, etc.
Interestingly, in my first semester at Trinity I had to write a personal statement of faith. Looking back at it the whole thing was pretty Arminian except for an strong affirmation of eternal security. So, it was sometime during seminary that I began to identify as Calvinistic. I know it wasn't until after a few years in ministry that I fully adopted the label 'Reformed' and the theology that goes with it (covenant theology, infant baptism, high view of the sacraments, etc).
Oddly, one of the main ideas that pushed me over the edge into Calvinism was the doctrine of ‘limited atonement' (the 'L' in TULIP). I prefer the label 'definite atonement' or 'particular atonement' (over against the Arminian notion of universal or general atonement). In many, that’s the last domino to fall. For me, it was one of the first.
John Owen argued 1) either Christ died for all the sins of all the people (universalism), 2) or some of the sins of all of the people (in which case, we’re all up the creek without a paddle, or 3) all of the sins of all of the people (the traditional Reformed perspective). Some countered that Christ died for all the sins of all the people but that this gift needed to be accepted by faith. Owen came back by asking if rejecting this gift was a sin (is unbelief is sin). If so, then did Christ die for that sin? If not, then your back to option 2 above (some of the sins of all of the people).
Anyway, you asked me what made me switch. That was one factor. There were others. For example, having accepted the doctrine of total depravity (which Arminius accepted also), one is left with the question of how one finds faith and repentance. Arminius posited 'prevenient grace' as prerequisite to faith. God offers this prevenient grace to all prior to conversion, making faith and repentance possible, but not inevitable. This grace is resistible.
So then, if all have received prevenient grace but only some respond favorably, the question becomes 'why?' Why do some respond with faith while others respond in disbelief. The answer can be articulated differently, but it boils down to something the sinner does. It takes the final outcome out of God's hands and puts it in the sinners. So the answer to 'why is this person saved and not that person' when both have received prevenient grace becomes, in essence, 'because this one is better (because he believed) than that one (who didn't believe)'.
The Calvinst says the believer believes because God gave the grace to do so; the unbeliever remains in his unbelief because God passed him over. Of course that raises different questions, but the believer simply cannot claim any credit for his salvation, so all the glory goes to God.
I 'switched' (from an inconsistent blend of Arminian/Calvinistic doctrines) to a more consistent Reformed postion because I believe, at the end of the day, the Reformed theologian accounts for the full range of biblical truth. The Calvinist scholars can allow all of Scripture to 'have its teeth', explaining how the different threads of truth are weaved together into a coherent theological framework. There are two ‘poles’ of text – those that emphasize God’s sovereignty in salvation and those that emphasize man’s need to choose. I think Reformed interpreters deal well with both; I’m less convinced by the Arminian treatments. Of course, there remain passages I'm puzzled by, mysteries I can't explain, etc. But on the whole, I think the Reformed position addresses these more fully.