imply it’s best to just be like everyone else

No it implies extreme fragility.

I think you’re not understanding the intended slam.

‘Snowflakes’ are special and unique. (Notably, their crystalline pattern)

Every snowflake is special and unique. (Every single one has unique environmental factors that form their unique shape)

If every… ‘thing’ is special and unique, no ‘thing’ is special OR unique.

It’s basically saying “you value your perceived characteristics higher than they actually are valued in the grand scope”

I can totally imagine an innocent couple sharing a cute nickname like snowflake and then having it ruined by the rest of humanity who are out here in the culture war trenches

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).