If I want to delete a question or an old answer of mine (I don't really care about if I lost my points or not), I'd like to be able to do this. I've been using this site since it was started back in 2007 and I've yet to see a delete button.
Because if there were to be a delete button it would get extremely annoying to see people asking questions the entire time and then deleting them constantly. That's what will happen. You'd know you can ask ridiculously dumb questions or offensive questions and delete them in a couple of minutes. Some people put a lot of effort into their answers as well and then it would all have gone to waste.