What are "self-insert" stories?

I see this argument used all the time but it's never consistent.



So we have the weak "beta" main character that powers up throughout the story, it's also called character development. Many standard shounen series have this type of MC. People bashing it call it "self-insert" so the so-called "loser otakus" can relate to the character because the MC starts off as a beta loser and gains power and a harem.



Oh no, so let's have an overpowered (OP) "alpha" main character. He's strong from the start so unlike the beta loser main characters, he doesn't have to work his way up the ladder fighting stronger opponents. He's usually upper-middle tier in that he's stronger than most but there are still a few top dogs that could beat him. But yet again it's called self-insert so the so-called "loser otakus" can imagine themselves as a super strong all knowing being. Tatsuya from Mahouka and Rudeus from Mushoku Tensei for example.



So if the main character is weak, it's self-insert. If he's strong, it's also self-insert. If he's a loser, it's self-insert. If he's an alpha harem king, it's self-insert.



Is the point of a story not to immerse the reader? If the reader can "self-insert" then hasn't the writer done a good job such that the reader can relate to the character they've written?



Why is "self-insert" being used as an argument?

What are "self-insert" stories?