I agree with you completely.

On the subject of the part about what's normal and not,

Nothing is normal, everybody has their quirks. Everybody who is "normal" is weird so everybody who's weird is normal, So for this reason, weird and normal are the same.

I know several people who aren't considered "Normal" by most that do things that make more sense than the social expectations of people who society as a whole considers to be "Normal".

Human behavior as a whole is very unpredictable, even without the involvement of mental illness, people considered to be mentally ill sometimes act more logically than those that aren't.

The reason why I prefer the word "neurotypical" to refer to "normal" people is so that I can avoid having philosphical discussions on the nature of "normalness" every time I try to talk about the difference between various mental disorders.

The reason why I prefer the word "neurotypical" to refer to "normal" people is so that I can avoid having philosphical discussions

Yes, but why use either word when neither one of them is accurate? 

There is no such thing as a "normal" person. Everyone, even people who consider themselves "normal", have certain quirks that separate them from everyone else.

Besides the world wouldn't be fun at all if everyone was the same.