Filch seems to hate students, dirty messes of Hogwarts, and pretty much magic in general. I know he is aspiring to overcome his Squibness, but there must be many better jobs than a janitor at a Middle-High school.
Why does Filch feel obligated to be a janitor at Hogwarts?
I don't think he really hates his job at Hogwarts. He really hates students, but he loves seeing them get punished. For example, he gets really happy when Harry et al. are going to the Forbidden Forest for punishment:
“I bet you’ll think twice about breaking a school rule again, won’t you, eh?” [Filch] said, leering at them. “Oh yes… hard work and pain are the best teachers if you ask me… It’s just a pity they let the old punishments die out… hang you by your wrists from the ceiling for a few days, I’ve got the chains still in my office, keep ‘em well oiled in case they’re ever needed… Right, off we go, and don’t think of running off, now, it’ll be worse for you if you do.”
They marched off across the dark grounds. Neville kept sniffing. Harry wondered what their punishment was going to be. It must be something really horrible, or Filch wouldn’t be sounding so delighted.
The fact that he's not allowed to use "the old punishments" bothers him, but it looked to me like he was just waiting it out. He did eventually get more freedom under Dolores Umbridge.
He does not fit anywhere else. He actually loves Hogwarts in his own way
We see squibs are difficult to find their place in magical world. Though apparently they want to belong. We see Mrs Figg living among muggles, but breeding kneazles to keep her connection with wizards. We also have Ron mentioning his mother's cousin who works as accountant (it is not specifically said he is a squib, but we can assume so giving the Weasleys are one of the most pure-blood families). Apparently he decided to fully mix with muggles and thus was excluded from magical society (as Ron said, now the Weasleys don't even speak of him).
Are all your family wizards?’ asked Harry, who found Ron just as interesting as Ron found him. ‘Er – yes, I think so,’ said Ron. ‘I think Mum’s got a second cousin who’s an accountant, but we never talk about him.
I believe for Filch getting a job in Hogwarts was a big luck. He is very bitter about being a squib and he obviously wants to belong to the wizarding world at least somehow (mind his Kwikspell lessons). Providing him with a job in magical society looks like an act of sympathy (something Dumbledore would do, though we do not know for sure who hired him).
Moreover, I think it's incorrect to claim he hates Hogwarts. He is very bitter indeed, but at the same time he is very devoted to his job and does it the best he can. He is nearly obsessed with keeping the school in order and harassment of the students seems like his way of fulfilling his responsibilities. He is undeniably very loyal to the school, he stays for the Hogwarts battle after all.
Did you ever wonder why Filch named his cat "Mrs. Norris"? Mrs. Norris in Mansfield Park lives with her rich sister's family, and once her nieces and nephews start growing up, they will be ranked higher than her. So she gets the Bertrams to invite a very poor niece to live with them, so now Mrs. Norris will always have someone inferior to her to bully.
Filch is at the bottom of the social hierarchy in the magic world, but at Hogwarts he can order the students around. That's why he works there. He doesn't want to leave, at least not unless he becomes a magic user.
Squibs in the magical world have a difficult life. On the one hand they cannot participate in the magical life, but on the other hand they will find it difficult to go off and make a life amongst muggles:
Different culture; they don't know how to dress or how to deal with everyday technology. How do you buy a muggle train ticket? Open a bank account? Use a credit card?
Documentation; this is becoming an increasing issue as the 21st century gets under way. If you want a muggle job you need identification papers to prove your right to work, and for most jobs they will want exam certificates too. These certificates also need to match school and exam board records in case someone gets nosy or suspicious.
As others have noted, Ron has a distant relative who is an accountant, so presumably he managed it. Maybe his relatives did some magic, for example creating certificates that confund anyone who reads them, to help him out. But its not going to be easy.
For a squib who can't or won't do this, the only work they can find is going to be low paid, low status manual work. Caretaker of a school is probably a comparatively good job for a squib, as is grounds keeper (Hagrid is not a squib, but being under a lifetime ban of doing magic is pretty much equivalent).
JKR spoke to this in a post on her old website. In short, Squibs often find it hard to fit into either Muggle or Wizarding society. Having a job gives his life purpose and allows him to be part of the wizard community, even if he's not a wizard himself.
Squibs would not be able to attend Hogwarts as students. They are often doomed to a rather sad kind of half-life (yes, you should be feeling sorry for Filch), as their parentage often means that they will be exposed to, if not immersed in, the wizarding community, but can never truly join it. Sometimes they find a way to fit in; Filch has carved himself a niche at Hogwarts and Arabella Figg operates as Dumbledore’s liaison between the magical and Muggle worlds. Neither of these characters can perform magic (Filch’s Kwikspell course never worked), but they still function within the wizarding world because they have access to certain magical objects and creatures that can help them (Arabella Figg does a roaring trade in cross-bred cats and Kneazles, and if you don‘t know what a Kneazle is yet, shame on you).
Filch doesn't hate Hogwarts, he is jealous that these kids are running around with magic that he should've been born with but didn't and then the kids make fun of him and so he doesn't really fit in any where. Hogwarts is like his home, he takes care of it and makes sure that the kids don't go misusing magic or be destructive.
