I can't find a proper verb corresponding to the adjective divisive. If a person is divisive, then can I also say that they "divide other people apart"? Is there a verb for divisive?
Upset would be the normal word to use. Otherwise
Disrupt (Merriam-Webster has a rather narrow view)
b : to throw into disorder "agitators trying to disrupt the meeting"
Sociologists also use:
alienate, antagonise, upset, dissaffect. estrange.
From the Oxford dictionary
Rift - verb: (usually as adjective rifted) Tear or force (something) apart
I'm not sure why divide doesn't pass muster-- yes, you can say "divides others"-- but when it comes to relationships between people, there's:
to split apart (an organization, two people, etc.) especially in a violent way
... which is most commonly seen in the word asunder-- "tear asunder"-- because sunder is such a rare verb. (Also sundry, so the root is still alive)
There is also cleave, but sunder has specific connotations for interpersonal relationships.
For verbs with adjectives, there's sows discord, drives apart, creates rifts, etc, but sunder is closest to what you want, albeit archaic.