fishing vs. hunting?

After a comment by a friend recently, I got to thinking about the difference between fishing and hunting. I can't believe I never noticed this distinction before! When I go fishing, am I not in effect hunting for fish? Shouldn't it be called fish hunting? After all, if I went and killed a dear or bird it would called deer or bird hunting. If that doesn't work, could we call deer hunting "deering", or call bird hunting "birding"? I think one of these alternatives is better than the current system. It is confusing me. Also, should we really call killing another human "murder"? couldn't it be called humaning? Ok, maybe I took that a little too far, but you get the idea.