I think the writers are using that kind of language to show the personality of that character. He doesn't want to admit (or can't see/believe) his girlfriend left him because he was a bad partner, and so explains it by saying she became a lesbian. By doing this he absolves himself of any blame, fault, or responsibility for the relationship failing.

From the US, as per the rule of the community.

• Generally as it's understood, yes, people are to a degree born gay. Although as it is now, it's up to chance and the environment around them if they discover it or not, as being straight is so normalized some never figure out they aren't straight, or if they do, it's later on in their life.

As to "becoming" gay, it really depends on what is implied with it, usually through context around the situation.

• If it's implied by the person saying it about someone else as being a decision, especially a sudden one, to just "be" gay, it's generally with an ignorant or sometimes naive perspective behind it, respectively thinking it's to spite them, just following a "trend", or just to get out of the relationship with an excuse, or alternatively, they just don't know better about how it really works.

• And if someone is saying they "became" gay about themself, it just tends to mean they discovered that they already were, or in many cases, became more open about it to others after previously figuring it out. Perhaps until that moment, they thought they were straight, or even bi or any number of other possible options, but found out otherwise and realized they were specifically gay.

• And finally, if it's considered offensive, it depends on that previously explained context, as well as the context of how it's framed within the series, whether it's just that one character that believes it, or if it's more widely held as a belief, and whether it's shown as a good or bad thing within the series.

• If it's taken 100% seriously, and isn't challenged as being wrong, either by being portrayed comedically as that character having awful views, or another character or some other means indicating as such, then there's the possibility of it being offensively intended, which goes back to it being naive or out of ignorance.

And for the TLDR variety, start here:

If it's actually played for comedic effect and/or looked down upon, then it's the character that is being offensive, and not the series itself.

• The problem indeed isn't that the girlfriend is a lesbisn or potentially bisexual, or that she isn't interested in him, which would go hand in hand with not being straight, but rather that she is cheating on him, which is itself a more complex matter, and doesn't necessarily attribute the fault to the girlfriend by itself.

• It could even be that part or even none of his claim is true if it's not otherwise shown to be, in which case it might just be him making up excuses for why his girlfriend isn't interested in him, when it's likely to be his personality or something else driving her away from him in reality.