I'm no stranger to OCs, personas, and alter egos. I'm no stranger to tagahanga works. I'm also no stranger to self-insertion. A lot of people on other websites I use hate self-insert characters, and especially hate self-shipping. Well, I think they're just wrong. Why is that? Because fandoms are for fun, interacting with canon characters is fun, and making mga kaibigan and falling in pag-ibig with your favourite characters is so much fun.
But first, why do people shame and hate self-shippers? Because they are pedantic and on their high horse about how tagahanga characters should appear and behave. These are the people who throw the term "Mary Sue" around and police how others' characters should look and act. They also throw around the terms "cancerous," which is super-inappropriate and rude, and "cringey." To be pedantic myself, cringey is not a word, and it is not a good critique of a character that could very well be the creator's first OC. And if it's their first-ever OC, it's very possible that the creator is a young person, either being a child or a young teenager. So way to go, you nitpicker, you're shaming a young person for not being as "experienced" in character disensyo as you, which is called "gatekeeping," my dear children, and is, in fact, frown upon in most fanbases.
But, Arynn-chan, why is self-insertion okay, then?
Coping mechanisms, my dear. I'm sure you have one. I do not have a good track record with relationships or friendships myself, becoming heartbroken so easily. But with fictional characters, I can be my true self and I can tell them everything I think without dirty looks. Because, as a lot of people think, self-shipping does not have to be romantic.
But romantic self-shipping is wonderful, too. For example, I ship my "persona," aka self-insert, with Marceline from Adventure Time. They're cute domestic nerds in all the things I draw and write, and they are very happy with one another. I think that their relationship is very innocent and cute, as they are both royals (my persona is the princess of cats) and they respect and pag-ibig one another.
Familial self-shipping is also wonderful. Like, if you do not have a good relationship with your real-life family, you can insert yourself into a fictional family. I personally do not do this, but I do have mga kaibigan IRL who do this.

TL;DR
Don't be a d-bag to people who self ship, bc you don't know why they ship themselves with their faves kthxbaiiii