Squidward's whole deal is that he was a scion of Old Money who got really into Marxism in college and decided he couldn't live with himself as a beneficiary of the Bourgeoisie. He cut ties with his parents and went to live as a proletariat for a few years to better his music.
Of course, what was supposed to be a short term service industry job before he lived for his art has bloomed into just being his life, and life as a poor artist is never as romantic as one imagines. While the cost of living of Bikini Bottom is low enough that even a frycook can be a homeowner, it's not quite so low that he can afford the luxuries he was used to growing up.
His view of the Working Class as the downtrodden masses were rather tattered by years of living between SpongeBob and Patrick, who were not so much temporarily oppressed intellectuals as they were, well, SpongeBob and Patrick.
Still, through thick and thin he's never gone back on his decision to leave the money behind. The great irony is that he is ignorant of his greatest achievement—his superiority to Squilliam isn't turning a bunch of randos into a functioning Marching Band or turning a burger joint into a fine dining establishment, it's having the strength of character to look at all the advantages Squilliam had and choose to leave it behind.
He will never be a master Clarinet player, but he will always have that
