Jane is really annoying. She's always teasing Ender in this way that is supposed to be affectionate but is actually passive aggressive and cruel. Okay, she has trouble with human social cues, but that doesn't change the fact that she ends up being rude and downright mean. Ender says he "liked her" (4.53), but Shmoop has trouble seeing why. She picks at him and picks at him, and then when he shuts her off for a second after she's particularly nasty, she throws a cosmic tantrum and essentially breaks up with him. Yes, it's true that she philosophically accepts his mistake (11.39), but whatever her claims, her actual response is to give him the silent treatment and never really be friends again.
All of that's forgivable: Annoying people deserve love and happiness too, and again, being a nice person must be especially hard if you're a computer. Shmoop gets that.
But then there's the fact that she betrays the entire Lusitania colony. She decides Ender will be better off if Lusitania and he have a common enemy, so she sets it up so Starways discovers that Miro and Ouanda have been giving illegal technology to the piggies. This provokes a crisis, and as so often happens in crises, someone gets hurt. That someone is Miro, who is paralyzed directly as a result of Jane's busybody shenanigans. She then becomes best friends with him, never telling him that she totally screwed him over. Why is that okay?
Perhaps it's okay for the final reason Jane is annoying—which is that she's not real. Of course, nobody in the book is real (um… it's fiction), but Jane is less real than the other not real things. She's just this voice basically, out there in the ansible, which spontaneously generates so that Ender can have computer super-powers. She's a literal deus ex machine—a god in the machine who comes in to save the day for the hero. Card needs Ender to be able to break into files, so there's Jane. Card needs Starways to know about Lusitania's naughtiness, so there's Jane. She's not morally responsible because she's just a plot device—she's Card's fingers on the scale. As sci-fi critic David Langford said, Jane is an example of "slipshot construction," who is "unnecessary to the main action" and "irritates" by solving all these problems for Ender like a smug magical genie (Source). She's this clunky, manipulative, all-powerful being that the book uses to keep things on track. It feels unfair and kind of dumb… or, in other words, annoying.
The problem, then, is that Jane is too close to Card—and perhaps, that Card is too close to Ender. Jane "paid attention to Ender Wiggin" (11.9), we learn, but she's not alone in doing so; the whole book pays close attention to Ender Wiggin too. Like Jane, the book is even infatuated with Ender Wiggin in all his overwhelming awesomeness as destroyer and healer and super-empath. Jane is one more superpower, one more sign that he's so awesome that even godlike computers love him. Shmoop thinks it's all just a little too much.