Must, may, might, can't (deduction)

When you are sure something is true: must
They must be out. There aren't any light on.

When you think something is possibly true: may/might
His phone's switched off. He might be on the plane now.
He hasn't written. He may not have my address.

When you are sure something is impossible / not true: can't
He can't be ill. I saw him at the gym.
They can't be Italian. They're speaking to each other in English.

We often use must, may/might, and can't to say how sure or certain we are about something (based on the information we have).
In this context, the opposite of must is can't, not musn't.