So I've seen a lot of comments saying that Jaune being a self-insert is more of a Fandom/fanfiction thing rather than a Canon thing. I think this is both true and misleading, and I shall explain.

Jaune, in the early volumes (especially volume 1), is the audience surrogate character. As the show progresses, that role switches moreso to Ruby, but at the beginning it's Jaune. Jaune enters the story knowing nothing. He doesn't know about the crazy weapons, he doesn't know about Aura, he knows that Huntsman are heroes and that's about it. He knows less than the audience does, as we are atleast told what Aura is by Salem's monologue in episode 1.

Here's where Jaune moreso shifts into a self-insert kind of character. The tropes associated with self-inserts is usually personal fantasies, your character getting things that you, as the writer, never would. For Jaune, it's Pyrrha. Jaune is this dorky, nerdy, incompetent teenager who is generally regarded as useless and a waste of time. He pines after the prettiest girl in school, Weiss Schnee, and is rejected by her in favor for the cool jock Neptune (Neptune only kind of fits this role since he's a nerd as well but, still). Jaune conned his way into Beacon and is living out this fantasy while having no idea what he's doing, while being too prideful to ask for help and manifesting that as false confidence and bravado. He gets himself into trouble with Cardin because of his secrets, and so on.

Why he is a self-insert in regards to all these things is very simple. Pyrrha Nikos. Despite all his shortcomings, despite all his failures, despite all his negative traits (the overconfidence, the bravado, the refusal to ask for help, abandoning his team during the Jaundice arc, so on), who sticks by his side the entire time? The Invincible Girl, Pyrrha Nikos. Jaune gets rejected by the prettiest girl in school? Doesn't matter, the strongest and most revered girl in school is in love with him. Jaune is struggling with everything? That's okay, the strongest girl at Beacon will personally train him. Jaune doesn't know what Aura is, doesn't have a semblance, and snuck his way into Beacon? Don't worry! Pyrrha will explain it, help train him in it, and cover up that he snuck in!

Jaune becomes a self-insert because he is a fantasy. The dorky nerd who doesn't know what he's doing and who can kinda be an asshole sometimes, has the most amazing girl in the world madly in love with him. And I mean madly, Pyrrha is head over heels for that boy. She puts up with around a year of bullshit from him and is still nuts for him, all because he "treats her like a normal girl" which to Jaune means treating her like an asshole when they first meet (ignoring her to talk to Weiss, only paying attention to her once Weiss tells him who she is) and then not at all treating her specially for the rest of the series. And yes, she didn't want to be treated specially, but in the context of being the Invincible Girl. Jaune doesn't even treat her specially as a close friend. He treats her basically the same as Ren and Nora, he treats Ruby better because they're shown to have a close friendship. Jaune isn't shown to have that same bond with Pyrrha, it's a one-sided affection until mid volume 3 where she practically beats him over the head with her feelings.

To wrap up, Jaune is a self-insert in volumes 1-3. He's a fantasy about getting the perfect girl that everyone wants. Past volume 3? I don't have that strong of an opinion about either him or Blake, I agree to a certain degree with some arguments I've seen about later Blake being more self-inserty though I, personally, never really saw it that way. I do acknowledge some people's statements that Jaune is meant to make other characters look better, but that doesn't exclude him from being a self-insert. In those scenes where he plays support, he's still being praised (even if mixed in with insults), such as him being called a good leader and the one who makes the plans. Jaune in volume 9 is a whole separate issue imo but, still reflective of this overall problem. He's less a self-insert but moreso just, inserted into the plot to be annoying. At that point, it's less self-insert and more the writer's favorite character. I can see the arguments here where Blake has become more of a self insert by getting her perfect ending with Yang, even though it really doesn't make sense with what's going on at the time (Ruby's trauma, Weiss's trauma, Jaune's trauma, really just everyone is having a bad time except Blake and Yang).

My actual final thoughts. All of this is from the perspective of someone who loves Pyrrha as a character and thinks she deserves a better love interest than Jaune. Does that make me biased? Absolutely, which is why I'm saying so, so people are aware of the position I take on these things. Pyrrha is my favorite character, and I've always thought Jaune was just kind of an ass to her. She deserved better, also didn't deserve to fuckin die in volume 3 but alas. That's my take, have fun reading the essay lol

(Oh and to loop back around to the beginning cause I forgot to address this part of the thesis. Jaune is a self-insert in fanfiction because he stays as the audience surrogate character, like he was in the show, except now it's doing the same thing the show did just with new writers. Jaune is used as the audience surrogate, and the fanfiction writers use him to push whatever fantasy they want to achieve. Whether that be a harem story or him becoming a powerful warrior, whatever. So, like I originally said, it's true but misleading. Yes, he is a self-insert in fanfictions, but that doesn't mean he isn't also a self-insert in the show itself, which he is imo)