The problem with saying people are "normal" is it's dismissive. I've heard this my entire life. "You're just quirky". I know people who say this are trying to make me feel better about myself, but here's the thing: I don't feel bad about myself in the first place. There's nothing wrong with being autistic.
Understanding that I'm autistic and what that means has allowed me to understand why I am the way I am, why I do the things I do, and most critically: how to work with what I have in order to live my best life.
"Normal" me couldn't manage very well at all. Autistic me understands sensory issues and meltdowns, and how to mitigate those issues in order to prevent the stress and overwhelm that leads to at best, discomfort and at worst, very bad situations. Autistic me understands my difficulties in understanding people's motives which allows me to make adjustments to the way I interact with others. This in turn keeps me safe(r). Autistic me understands that I don't communicate the way others do, and this allows me to be clear about what my needs are when communicating with others, so that we can bridge the gap between my communication style and theirs. Autistic me understands that I don't know my own emotions all that well, and that I need to put in effort - by putting in that effort, I can greatly improve my life.
These are all greatly positive changes which were withheld from me by insisting that I'm normal. Understanding that I'm autistic allowed me to work with these things and find a way to work around them or better yet, make them work for me. I couldn't do any of that when I was trying to see myself as "normal" and not understanding why I was failing so miserably at things that others found effortless. Recognizing that I'm not in fact normal, has afforded me a great deal of self compassion that I wasn't able to have before and has released me from a lot of shame that I carried as a result of the things I couldn't seem to get right.
Being "normal" isn't a good thing at all, in my case.