That’s a tricky one for me because I see a lot of utility in asking for sources:
a) Curiosity. Maybe I really want to know how this person came to believe what they did even if I’m pretty sure they’re wrong.
b) Challenge. A version of the Socratic Method, helping them learn through questioning their assumptions.
c) Learning. A genuine quest for knowledge, that perhaps might yield more unique or varied results than Google.
d) Depth. Possibly helping others in a public thread (or the author) realize that it might be an epistemically illegible argument requiring greater scrutiny, discussion or evidence.
I get that asking for sources can also be lazy or ill intentioned, but for the most part I don’t mind it.
Much of the time it isn't fair to ask for citations even for specific facts, but that's a separate problem.
Those cases are covered by b)
But the person you're replying to pointed out other, non-adversarial reasons to ask for citations (which depending on the tone of the question, may be misinterpreted)
It seems like being clear about what you're doing (are you just discussing possibilities or trying to claim something specific) would go a long way in avoiding such misunderstandings.
(And I of course don't know which cases you're talking about, so I'm just talking about possibilities.)
I was pretty relieved when I got to Philosophy, where no one gave a damn about anything but the argument.
At first, it seems odd to me that your English professors acted in the manner you describe, but I guess most of them have chosen to ride the criticism wagon, rather than the creative one.
If there is going to be a standard for legibility, there should be one for literacy too - it's especially important when learning from a debate where readers and writers (or sources and sinks) switch roles, to understand how different positions are engaging with each other's arguments, not just how they are making them