"depression and suicide", "Don't question their mental fitness." Gender dysphoria is linked to mental illness for a good reason like depression and suicide being linked Being honestly concerned about such is a sympathetic reaction (empathy is the wrong word unless you're also transgender) that I would expect.
As someone that doesn't identify as a traditional male I've seen some pressure to to conform with with the tradition male gender role and it is very uncomfortable. This push can confuse some people into thinking they are trans when they just do not fit stereotype. For someone that is trans the pressure would be even worse as they would be constantly pressured to act in a manner contradictory to their nature, and that big push is something you failed to even mention.
Also I have no problem using the pronouns that someone wishes, but pushes to require it or punishing people for not iding it as a single glance is a a suppression of rights. Also some women have been victimized by "trans" women that have been allowed in their spaces.
The issue on the whole is not as simple as either side wishes to present it as