"Why not" is the equivalent of "Why shouldn't one" or "Why shouldn't someone". "Join" is acting as a verb in this sentence and, therefore, must be conjugated for the third person "someone". "To join" is the noun equivalent but we already have a noun in this sentence--"someone"-- which means that "join" is the verb because we must have a subject and a verb for the sentence to be syntactically correct. You could use "to join" as an infinitive verb if you have another verb in the sentence. For example: "Why do you not want to join?" "Why do you refuse to join?" For more reference to verbs as infinitives, see: https://www.ef.edu/english-resources/english-grammar/verbs-followed-infinitives/

See rule #6 under bare infinitive. https://www.myenglishpages.com/site_php_files/grammar-lesson-infinitive.php

Thank you very much, Evan!

I was born and raised here in the States and I tell ya, that's a good question! Never thought about it. If I had to venture a guess, I would say that the verb "join" simply does not always need the preposition "to" for instance you can say "the men can join the club" and it would be wrong to say "the men can to join the club". I think in short the preposition 'to' implies future tense. And thus when you ask "why not join" you're talking about the present, not the future. If you did want to talk about the future, you would say "... Why would you not want to join..." That sentence is correct, although a bit wordy but if you must have the preposition "to" that is a way to add it correctly. Otherwise, just speak in the present tense, drop the to, shorten, move on. I'm submitting this as a comment, not an answer cause I could be completely wrong, I'm just guessing here! But hopefully it helped somewhat.