“Normal” is a social construct that hardly anyone probably fits into. Most people have at least some major traits that diverge from the average.
The reason people dislike the use of “normal” is because it’s usually used with the connotation that being outside of whatever is being described/considered as “normal” is bad, and describing a group as “abnormal” is usually meant as an insult and used to dehumanise.
I’m not ashamed of being trans regardless of whether it’s “”“normal”" ^.^, and I don’t think being whatever our society deems “”“normal”“” is even desireable - though as I said before, most people are likely outside society’s definition of a “”“normal”“” personl in at least a couple categories.