The weirdness is that the prefix suggests no direct object, but the {-moH} seems to require one.

-moH does not require an object of any kind. Its description says simply that it means the subject is causing something. It doesn't say anything about objects. All it means is that the subject causes the verb instead of doing the verb. And then we have examples like maghoSchoHmoHneS'a' may we execute a course (to some place)? in TKD and SeymoH QeH anger excites in TKW that back up the idea that an object is not necessary.

The {-choH} is probably unnecessary, unless your focus is on the fact that we are BEGINNING to cause each other to be angry. 

This is my understanding of what mayqel is asking for. It's not an answer to why we always make each other angry; it's answering how we got into the state (-choH) of being angry. The -choH is needed for that. The confusion is entirely from the English sentence: does we anger each other mean we get each other into an angry state, or does it mean we are angry whenever we are together? I would be more inclined to think he means the former, and his Klingon sentence backs up that belief, but either is possible.

-- 
SuStel
http://trimboli.name