John has seen Rose at her absolute worst.
During the events of Seer: Descend, not only was Rose overcome by the Horrorterrors and hissing and spitting like an eldritch cat, she may have been suicidal. Her lack of concern for her own well-being was already becoming uncomfortably prominent when she first mentioned her plan to deliver the Tumor, but in her conversation with Jade that revealed her mother’s death, it’s clear that did not care about what might happen to herself at all. When John met her she was possessed not only by the Horrorterrors, but her desire for revenge and her absolute lack of care for her own safety.
Flash forward three years: while Rose has gotten over this unhealthy behavior, she has been consumed by a new unhealthy behavior. The drinking was only the tip of the iceburg, for her conversations while drunk reveal that she not only does she lack concern for herself, she has a deep-seated self-loathing. She thinks she’s stupid. She thinks she hasn’t been a good Seer of Light. When John finds her, not only is she hungover but she’s very, very frustrated with herself.
And yet John still sees the best parts of her.
He most certainly isn’t oblivious to her bad parts: he knows she’s been overtaken by her “stubborn throes,” he doesn’t shy to tell her that her supposed “heart felt” messages are pretty weak—and if he spent enough time catching up with the Meteor Crew to learn about Dave and Terezi’s past relationship, it’s not too much of a stretch to suggest that he probably learned about Rose’s drinking problem during the last year.
He’s not oblivious to her faults. He accepts them.
He very well knows that she’s human, she makes mistakes—and he still cares for her. He knows that her drinking problems don’t erase how smart she is or how much she helped guide him to grow during the early stages of the game.He knows that her fit of grimdarkness doesn’t negate the fact that she’s a nice nerd who gave him a bunny for his birthday.
He knows Roxy shouldn’t be nervous about meeting Rose Lalonde, the girl who tried to break Sburb, the girl who was possessed by creepy calamari aliens, the girl who obliterated an entire castle in a fit of rage. Because he knows what’s more important than her failings is her triumphs, and that is why she is his friend.
Because even at her lowest points, he can still see the nice nerd who likes to read and knit.
And that is friendship.