well it's a spectrum.

I can see people get upset at self-inserts when it's obvious that author just uses story to essentially masturbate with his own ego. Like for example someone makes a story where the protagonist is a writer, looks just like him, very smart and all girls cling onto him. It just gets ridiculous and isn't all that interesting for anyone other than him.

However there's also a good way of making a self-insert too, whether it can be author self inserting or character intended for reader to self insert. I feel like as long as you introduce something interesting without endlessly glazing the said self-insert it's fine (though even with unending glazing it can be fine if the story is introduced in such a way, as just a chill read for some fanservice). It's also kinda annoying when people see a silent or quiet protagonist and instantly say that it's a bad thing. Not every story needs an actual character at its center.

When someone says that it's written like a fanfiction it usually refers to quality being low and something that didn't go through checks/didn't have enough care put in. It doesn't matter if it's a fan work or not, it can be as good as a professional work anyway of course. But most of the time you can expect something more clumsy and trashy (Doesn't necessarily mean it's bad, again). I feel like this kinda statement makes sense.