"Have to" vs "Don't have to"

[johnny 5.65]

A student has asked me a tricky question the other day, that I would like to be able to answer better shall it arise in the future. Any help, is greatly appreciated. The question is as follows:

Since “must not” is the opposite of “must”, I thought “don’t have to” is the opposite of “have to” but I got it wrong on the test. Can you help me.

[trousy]

Explain him their meaning is different:

Must not: Prohibition => I must not chew gum in class or the teacher will tell me off.

Must: Obligation (normally moral or imposed by yourself) => I must go to the supermarket - I want to make my mum a favour.

Have to: Obligation (normally imposed by another person) => You have to go to school from Monday to Friday (whether you like it or not).

Don't have to: Lack of obligation => You don't have to wash your car, it's clean enough (= you may, but it's not necessary).

Regards.