Arguing based on past experience is all well and good, but, in my opinion, defending something on a theoretical ground rather than simply "it didn't work last time" is always beneficial. Only one person, iirc, has mentioned the primary reason for separating church and state: conflicting interests.
In the end, government in a democratic society exists only to represent the will of the people, and to act in their best interests. As soon as they are beholden/answerable to other, religious, faith-driven obligations - for example, Catholics are answerable primarily to the Pope, hence Britain's raging hate-rection for Catholic politicians - their impartiality in acting in the interests of, and according to the will of, their country's people is questionable. 
There's a freaking tonne of other arguments, but that one's my favourite because I get to talk about "society" a lot, and as a young and naive teenager nothing gets me off quite like talking about lofty ideals of rights, and "the people".