The answer is multifaceted:

1) Because that's how people do it. Sometimes we all collectively settle on a standard that isn't the best, but that's just how it's done.

2) It allows for more easily expanding to multiple pronouns, e.g. "he/they" or "she/they", which indicate that the person is ok with "she/her/hers" or "they/them/theirs".

3) It makes it easier to state neopronouns (e.g. xe), by standardizing the form -- he/him/his is the same format as sie/hir/hirs or xe/xem/xems.

4) (My opinion) It feels more natural to say "he him" than just "he". "What are your pronouns?" "He." I dunno, it's a short enough utterance that it could be easily to mishear?

So you know how to refer to them to other people or in conversation. The order notes preference. So someone might use they/him, which means they prefer you use ‘they’ but if you use ‘him’ it’s okay.

Eh it's just arbitrary convention we landed on. You're right that it's redundant (as opposed to just "he" or "she", for example).

You will sometimes see people write something like "he/they", but that just means that either are acceptable.

It is redundant for the common pronouns. But once you step outside that space, people may need to see both. E.g., "they/them" is in the process of becoming established, so some will need the pair. And if somebody is using one of the neopronouns, most people are going to need to see both: https://en.wikipedia.org/wiki/Neopronoun

This redundancy is quite irritating to me. For most people, their pronoun is simply "he" or "she". Showing other parts of speech is only necessary for nonstandard pronounds.