So you start writing, let's say a silly little self-indulgent meta-style fic where you get to meet one of your favourite fictional characters. Good on you, have a blast.
But this person on the page, she's doing something you've never done and never will and never can - meeting one of your favourite fictional characters. You're having to imagine for her a set of circumstances that would allow this to happen, which puts a level of distance between you and her.
And even if circumstances very like those that happen to her do end up happening to you* in real life, they won't unfold the same way - they can't, because, well, fiction. Because those circumstances won't unfold the same way, you won't react the same way. But even if they somehow could, you still wouldn't react the same way, because you've already considered how you would react in those circumstances in order to write the self-insert, and you have that knowledge informing your actions.
Depending on how the story unfolds, you may have to research and learn about things that you can't let your self-insert know about, because she's supposed to be you, and when you started writing this story you didn't know any of those things. And even if you deliberately write her learning all the things you learn along with you, at some point, the story will end. You'll move on, you'll change, you'll grow. She never can, and at some point, you'll look back at her and realise that no one who knows you now would ever recognise her as you.
Even writing in a self-insert cameo as The Author within the text necessarily creates a level of distance between you, the author, and the character of The Author, who now exists in and can be acted upon by the narrative. You can slice it so thin you almost can't see it, but you can't ever actually breach that barrier.
No matter how close to life the self-insert gets, there's always that rupture, and it only grows wider the more story gets told. You can't be in the story and still tell it. But isn't wanting exactly that part of the whole impulse to tell stories in the first place?
*yes, this has happened to me. It's not actually uncanny or anything, I just deliberately wrote a plausible circumstance that I might get myself into to base the self-insert fic around. But it sure felt uncanny at the time.