Why do you need spaces in the password? Honestly never ever thought about using spaces in the password.
Why would they disallow it? It’s just a character like everything else.
UX. People accidentally adding whitespace by copy&pasting it. Easy to overlook and probably lead to some customers being confused. Also people use whitespace to separate words in text. Most password managers don't generate passwords with whitespace by default.
Disallowed characters like that give the impression that plaintext passwords are being stored.
Besides what others said: Passphrases like the famous "correct horse battery staple" https://xkcd.com/936/
I think the better question is, are they the only ones not taking passwords?