Snowflake is such a weird insult as it seems to imply it's best to just be like everyone else

Doesn't the same apply to pretty much any insult?

And why we're not supposed to use the word "normal" when referring to somebody or what they aren't..

I don't think snowflake is intended to be an insult though, is it? I always thought it was a stupid reference to what is perceived as an over sensitive generation (or person).