Must and have to are similar in meaning. they are both used to describe obligations. however, their negative forms are completely different in meaning.
we still use mustn't to talk about obligations. for example: in the house, i mustn't wear shoes. you know, to keep the house clean.
but don't have to does not describe obligations, so the choice is yours! for example, if your teacher said: you don't have to do your homework, well... then choice is yours. you can say: alright, i won't!