He must love her.

[keannu]

1. He must love her.
2. We must love our children.

In 1, "must" is a certainty, meaning "I'm sure he loves her"
In 2, does it mean obligation like "We have to love our children"?
As for "must", when coupled with "state verbs" like "be, love, like, hate, etc", does it always mean a certainty or sometimes obligation?

 

[Raymott]

'Must' could have all of its possible meanings in both sentences. This should answer all of your above questions.
(You first assertion is therefore wrong.)

 

[keannu]

Okay, then "must" means certainty only when coupled with state verbs like "be, like, hate, love" must be wrong. Also, "obligation" with "action verbs" like "go, throw, call" must be wrong, too.

1. She must be home now. If she goes out, she will be killed by terrorists surrounding her home.
2. She must be home now. As she worked so hard, being so much drained now.

So in 1, it can mean "certainty", while in 2, "obligation", so is it all the matter of context?

 

[Raymott]

“She must be home now” – I just rang her home number and she answered. Certainty.
“She must be home [by] now” – She left 30 mins ago; she lives 15 mins away, and she said she was going straight home – High probability
“She must be home now” – If we knock on her door, and she’s not home, she doesn’t win a prize. – Obligation. (She’s obliged to be at home if she wants to win the prize).
The lights are on. – A deduction that might or might not lead to an inference that she must be home now. – possibility.
She’s on home detention. – Obligation

Yes, it's pretty much a matter of context.