“I can’t talk right now” is a complete message. It doesn’t need a reason attached.

Explanations invite negotiation. The moment you attach a reason, the reason becomes the thing to argue with, so now you are defending the size of your homework instead of the simple fact that you are not free. A short answer with no handles on it is harder to pull at, and it is not rude.

Try it once this week when you genuinely cannot talk. Say you will come back to them later, then actually do. People who care about you will be fine. Anyone who demands a reason has just told you something useful about how they treat your time.