Heya, Arshi. (-:
I've definitely got some guesses here.
I think a big part of the problem is that the main associations people have—both from real life and fictional sources—with mental illness are some of the more extreme or concerning kinds.
Psycho- and sociopathy, sexual aberrations, schizophrenia, etc.
Heck, even with people who do suffer from some of those issues, there are different levels, and you wouldn't want people to assume that you're evil or serial-killer material because of a diagnosis that may be nowhere near that bad.
Let alone with people who have other types of mental issues like anxiety or depression. When people hear about mental illness, they may be picturing someone who's hallucinating or delusional, or whose words and perception cannot be trusted. None of that is anything you'd be in a rush to have people associate with yourself.
Additionally, there are other issues with the perceptions people have. There are portrayals that are harmful because of their inaccuracy or dishonesty (like normalizing or glamorizing unhealthy conditions or behavior), plus there's the issue that people may not realize that not everything fits a certain mold. As an exmaple, not all depressed people are doing anything as classic or apparent as sitting in a bar all day listlessly drinking alcohol and staring at pictures of a lost husband or wife. In fact, people can have very substantial depression yet also be quite functional and even show a great deal of cheerfulness (it may be faked but can also be genuine!) & mirth.
And an additional reality is that there are indeed very legitimate problems and dangers associated with different mental issues. Frankly, people are more than difficult enough to deal with under typical circumstances! So it makes sense, whether in a business or personal context, that people may not wish to admit to any additional obstacles they have that could be problematic and put people off, much as with purely physical issues/disabilities.