I theorize that the fragile straights aren't actually straight. Which I assume is what the developer is poking fun at with the quotation marks.
Our social default is still to assume that most people are straight. It doesn't make sense for a straight person to have a driving need to prove that they are straight ... unless they think someone would have a good reason to put them into a "non-straight" category.
I mean, I guess depending on context? This really isn't about static titles though. Like, nobody fought for straight people to be allowed to exist. Even in our modern age gays are still executed for being themselves. It's understandably offensive if someone is like "I want to show pride too!" if the thing you're proud of is winning the right to openly exist and the thing they're proud of is... being the more socially accepted and advantaged class?
It's not a perfect comparison but it's almost like if a rich person wanted a trophy for being rich because the lower class just got a trophy for surviving being poor.
Being offended by somebody "calling themselves straight" is stupid and fragile.
Being "proud of being straight because somebody else is proud of being queer" is stupid and fragile.
Being "content with being straight and wanting to label yourself as such in an environment where that makes sense" is reasonable.
I dont play the game so I dont know the context but I assume labeling yourself straight does not make sense in a fishing game and as such it is most likely about the second point
Because people like to express themselves. Were social creatures. You'd might as well ask why hats or different coloured fishing rods are part of this fishing game.