Tell My Mother - I Feel Fine

They are not emotionless - all Vulcans have emotions, even if they all are tutored and instructed from early childhood not to express them and techniques, with a basis in Vulcan psycho-social biology, in how to suppress them.

But Spock is not fully Vulcan, so techniques can never be fully effective in his case - he can't fully purge himself of all emotion using Vulcan techniques, although he does try at one point to do so, before realising at the last moment how the attempt itself is wrong and futile, at least in his case, and he must find his own path.

It's a Social Taboo - as a Vulcan, Sarek was raised to regard all expressions of emotion as obscene, even though he has and experiences his own emotions all the time, which he reflexively ignores. But, as an ambassador and a husbamd, he respects and is tolerant of emotional displays by aliens.

The problem is that Spock looks Vulcan. And he is his son.

Any open expression of emotion by his son would seem innately obscene and repulsive to Sarek - that's why they don't get on.

And yet a Statement of Fact is perfectly fine.

And Spock's non-Vulcan emotions are a fact.

And, Sarek loves his wife. As only a Vulcan can.

That's why, the key exchange of this conversation is when Sarek compliments Spock on his choice of associates, to which Spock responds with the statement "They are my friends."

The momentary pause before Sarek responds with the acknowledgement "Yes, of course.", carries all the meaning.

He knows, obviously he knows, but is almost incapable of openly admitting as much in his own terms.

And Spock by now has learnt enough about himself than to know better than to embarrass his father.

They are both right.