First of all, there's a danger in assuming that everything an artist writes is meant to represent their thoughts on a topic. Just because it's a song doesnt change the fact that the narrative content is fictional (or "inspired by true events").
Even situating the point of view as first person doesn't mean anything, necessarily, no more so than a stand-up comic prefacing a ludicrous story with "This is true!". Is it? Maybe, maybe not. The authenticity of whether it reflects the author's lived experience or not is irrelevant in the face of "Is the joke funny?". Point of view is, at the end of the day, a storytelling device.
With The Outsider, I think there are lots of different interpretations. In my personal headcanon, I've always thought that the song's title refers to the narrator, not the character suffering from suicidal depression. I think the lyrics imply this situation has been going on for a long time, and the narrator is at the limit of their empathy. They care about the depressed individual, and they've tried in the past to help (in so far as they understand it), but, because they are an Outsider to that headspace, they literally cannot understand the victim's plight.
Perhaps you have a bottomless supply of empathy and you are able to ALWAYS react in a sensitive and caring why when someone trauma dumps on you (whether you consented to it or not). If so, congratulations, and please tell me your secrets. However, there's a reason that advice for helping people with their emotional issues almost always starts with taking stock of your own emotional needs first. Sometimes, no matter what lovely and benevolent people we are, we just aren't equipped to deal with someone else's cross to bear.
Now, I hope that the outcome of that situation is something other than "if you're gonna kill yourself, stop talking about it and do it somewhere else". Even still though, is that hugely different in spirit than people saying suicidal individuals shouldn't traumatized other people with their actions? Obviously not a 1:1 comparison here, but think of any instance of suicide by cop or a mass shooter that blows their brains out at the end of their spree. I guarantee there will be people sadly wondering why they couldn't have just driven off into the woods and blown their brains out like a civilized person.
Additionally, because this is a 3 minute song, we don't know if this is the final resolution of the relationship, or if it's a momentary lapse in the narrator's empathy. Have you ever snapped at someone and said or did something you didn't mean? Would you feel it was fair that single outburst became your entire public persona forever more? Probably not. I don't know if that's how Maynard intended it, but, frankly, I don't give a shit. This interpretation is truthful (and meaningful) to me. Maynard's interpretation, if he has one, is interesting information, but almost completely irrelevant to my enjoyment of the song.
To get out ahead of it, this depends on the outburst, before someone comes in here and misconstrues this to mean I'm implying I think Mel Gibson or Laura Schlesinger deserves another chance or something equally dumb.
Finally, for the sake of completeness, I could also make an argument that "The Outsider" refers to the suicidal individual who exists outside of the paradigm that the narrator has about life, and I could also argue that Maynard is the outsider, simply observing a plausible relationship dynamic from afar. Finally, sometimes I wonder if "The Outsider" is a voice in the depressed individual's head, essentially beating themselves up for wanting to die but not having the "courage" to pull the trigger, as it were. Frankly, that degree of ambiguity is likely intentional. As folks have mentioned, Maynard has more than a little troll in him. This is, after all, the guy who sings about overanalysis being the death of intuition and the spirit, while also structuring the number of syllables he is singing per phrase to match the Fibonacci sequence.
Sorry, wrote a lot, but The Outsider is a particularly meaningful song to me, and the apparent callousness of its lyrics is a subject I've ruminated on before.