This phrase is kind of ambiguous. Some people actually mean separation of church and state, while others mean separation of religion and state, or perhaps even separation of religious morality and state. If you want to make yourself clear, refer to something more meaningful, like the part of your constitution/law regarding laws about religions. The following writeup is somewhat muddled in definition, but I hope you can extract my message. I seem to be treating it as a single idea that we should either take fully or not at all.

There are so many reasons why this separation is a good thing for even us Christians:

  • Churches don't need extra power. Their duty can be accomplished just fine as merely a meeting of people.
  • Avoiding infiltration of politics into the church. Without the separation, not only would goverment become a tool of the church, but the church would be a tool of the government.
  • Freedom. If there is a quibble within the church, you should not get a forced silencing of one side. You may be called a heretic, but you are not burned. The separation is especially good if the leading theology is crazy (see previous item).
  • ...
I could go on with the specifics, but I'll just say that these two organisations do not work together. Constantine screwed up things pretty badly, in my humble opinion.

On one hand, we want a law that says "do not kill", yet we want to lawfully allow people to be selfish in their choices, which is just as much a condemning sin as murder. The conflict between allowing people to be selfish and giving other things precedence has resulted in a few controversies. Perhaps the basis of our laws should be secular morality - to leave the judging to God.