What kind of character is Longtail?
Reasoning and Evidence
Well, in the first book, he's perceived by most readers as an arrogant jerk. At the time, I felt that way as well. But really, he's a much deeper character than you'd expect.
In the first book, he challenges Bluestar's decision about letting Rusty into the Clan, and I don't particularly blame Longtail. The Clans are proud and strong, and don't need kittypets.
Longtail, at the time, was likely a proud young warrior who cared deeply for the warrior code and ThunderClan, but expressed his opinions using violence and arrogance, though I think that is to be expected in young cats. The Erins use personification on the warrior cats a lot to make inhuman characters seem more relatable, and I find this ingenious, since it cleverly explains so many events in the books.
In Longtail's case, he was an adolescent, and humans at that age tend to have outgoing yet brash personalities. Human teenagers are very protective of what they value, and apparently so are the warrior cats.
When he fights Rusty, I think he's not being arrogant and selfish, but rather protective of his honor. I think it's also to prove to Bluestar and his Clanmates that he is an able warrior. Bluestar had said that there had been few apprentices to train, and they needed more cats, and I think this sort of deflated Longtail while filling him with adrenaline, in a way.
He was disappointed because he wanted to carry his Clan through many hardships, and he likely felt a kittypet could not save the Clan if he couldn't. He fought Rusty to prove his own strength, knowing Bluestar likely thought highly of Rusty for some unexplained reason at the time.
When Longtail lost his eyesight, I believe it was a major blow regarding his self esteem and his honor, which explains why the fiery young cat seemed so droopy and calm after the incident. He wanted still to serve his Clan, but did not believe he could as a warrior or a medicine cat.
It's happened in many instances, actually, so I can't help why he didn't become a medicine cat. I think it might have been because he was afraid of hurting someone or making a mistake, like he had made a mistake and lost his sight to the rabbit.
Then again, it could be because he fell into a state of depression after his accident, and the life of an elder offered comfort and fellowship compared to the isolated existance of a medicine cat.