Here is an example of "no" used as a complete sentence:
"Are you coming to the talk tonight?"
Simple, but it never feels this simple. For some reason, we can't accept no as a complete answer to a question. Yes is a complete sentence. If you replaced the "no" with "yes" is the above conversation, it would sound fine. If your answer is yes, you don't need to provide an explanation for why you are going. Yes can be followed by a period, but no is always followed by a comma and then a reason for not going. But you don't owe anybody an explanation for why you're not doing something. No is a complete sentence.
I really hate it when people complain about other people's stupid excuses. People wouldn't have to invent so many stupid excuses if it were perfectly acceptable to just say, "No, I'm not going/not joining/not interested," and leave it at that. No one has an obligation to do something just because they can. People often denounce the "I don't have time," excuse, saying that the person does have time. But I always assume that someone might choose to take an easier course load or a less busy job because they want that extra time for themselves. If anything, I would assume that a person who is involved in a lot of things already would be more likely to join something else because they clearly like to be involved in a lot of things. I would also guess that a person who is involved in fewer things (or nothing at all) would be less likely to add something new to their schedule because they probably don't like to be busy. And saying that a person who doesn't do as much should do more amounts to peer pressure, which is not okay.
No does not require an explanation. No should not be followed by a comma, but by a period, because no is a complete sentence.