I must go home―old fashioned?

According to a friend of mine, "A native speaker says it is an old-fashioned way to say, 'I must go home'." According to my friend, it should be "I have to go home."

I wonder if this is true.

In my understanding, there is a slight difference in meaning between "must" and "have to."

If I say, "I must go home," it means I am going home and it's not against my will.

If I say, "I have to go home," it means "I am going home whether I like it or not (it may mean I am going home against my will).

Am I correct?