Learn Hardcore Latin: Patri displicet quod frater amicis suis non parcit verbis iratis. - Father is displeased that the brother does not spare his friends with angry words.

Because displicere works like to be displeasing to someone, not like English to dislike. In Latin, the person who experiences the feeling is often put in the dative with verbs like placet and displicet.

So:

patri displicet = it is displeasing to the father
more natural English: the father is displeased

What is the subject of displicet?

The subject is the whole quod clause:

quod frater amicis suis non parcit verbis iratis

In other words, the fact that the brother does not spare his friends angry words is what displeases the father.

This is why displicet is singular: a whole clause can act as a single idea or fact.

What does quod mean here?

Here quod introduces a clause meaning that or the fact that.

So it does not mean which here. It is not a relative pronoun in this sentence. Instead, it introduces the content of what displeases the father.

A good way to understand it is:

Patri displicet quod... = The father is displeased that... / It displeases the father that...