The whole construction of the question is overly verbose. When you ask a question looking for an answer, the entire sentiment of "can you tell me" is implied. Let's remove it.
As mentioned in a comment below, this does not make the question any more/less correct. The reason we remove extraneous content is to reduce the risk of misidentifying the portion of the question that contains the error/confusion.
- why to do?
- why not to do?
There is no object in these questions, so let's add one and see what happens:
- why to do my homework?
- why not to do my homework?
There's also no subject in these questions, in which case, the implied subject is the person being asked, in other words "you". In this case, I'm going to assume that you mean for the subject to be your self, so:
- Why I to do my homework?
- Why I not to do my homework?
The question is obviously very confusing at this point. What form should the answer take? I think in this case you want reasons why it would be beneficial to do/not do whatever it is. That's what should means. You can replace the word should with "would it be beneficial if":
- Why should I do my homework?
- Why would it be beneficial if I do my homework?
- Why should I not do my homework?
- Why would it be beneficial if I don't do my homework?
The confusion in the original case comes from lack of subject and object, but when we add those, tense becomes harder to deduce. 'To do' means future or hypothetical, so you may be asking 'why will I do my homework?' (a question only you can answer), or 'why would/should I do my homework?' (clearly hypothetical).