A debate has rules which must be conformed to. Each participant has a time limit which they need to keep to and generally personal attacks must be refrained from, meaning that you cannot assault the way of life of your opponent for any trivial reason. An argument is a verbal brawl which could easily escalate at any moment.
If you have a dream about a debate it means that you need to think about the fact that you have been getting into a lot of arguments lately. This will be especially true if in the dreams you are one of the more aggressive people in the argument. You want to have a dream in which you are not the aggressor, but in either case it means something bad. Either you are too aggressive towards others in your life or you are not aggressive enough and you end up getting walked all over. No result is really a good one and it might be hard for you to come to terms with this, however you will need to if you hope to get past the dream and live happily.
A debate is a way of civilly discussing a difference in opinions that you may hold. If you have a dream in which you are part of a debate this might mean that you’ve been angry recently. But your brain is trying to let you know that the best thing for you to do now would be to argue it out in a more civil manner before you get yourself into trouble and danger with your temper.