You have to go home - Musíš jít domů. There is a difference in it. Muset = must is a situation in which you are forced by circumstances or somebody's demand to do something. Mít + verb = supposed to , be to +verb is a request and it is up to you to decide if you are to follow it or not.
I understand that HAVE here does not imply ownership, but in the English phrase: "You have to go home" have does not imply ownership either, which is why I thought that maš --> have to would be OK. But, as I often said, I am deaf to the subtle nuances of Czech. Hopefully, one day that will change.
So here's the thing, it seems to me. What we are learning here is that the mít-plus-infinitive construction gives us "supposed to" (whatever). While we can carry it around in our heads in other forms, we ought not to overlook the teaching purpose of the exercise. And, with that, off the soapbox I go... :-)