COCKRUM: “Kind of at the last minute. The way this all came about was that when we were first planning out that first issue, we decided what we were going to do was have it be an aptitude test or an entrance exam or something like that. They would be sent off to rescue the original X-Men, but the original X-Men would not actually be in any danger. We figured if it’s an entrance exam, theoretically, there are people who are going to flunk as well as people who pass, and so we had Banshee and Sunfire, and we were going to flunk ‘em. Then we thought, well, that doesn’t seem fair, we ought to have a new guy to flunk too, a new guy who’s unsuitable. So that was what Thunderbird was for, to be a flunker. He was unsuitable because he was anti-social. Hah! As if Wolverine’s not anti-social. But at the last minute--well, I liked Banshee and we all liked Thunderbird, so we figured to hell with it. It turned out not to be a test anyway. So we had Sunfire, who nobody much liked, go off in a huff, and we kept Banshee and we kept Thunderbird. But then we didn’t know what to do with Thunderbird because we never thought him out. It was easier to kill him off than to think him out.”
First, Thunderbird's creators conceived him as an anti-social misfit. A classic angry military vet. A stereotype.
Second, even when they decided to keep him, they had no idea what to do with him. Which isn't surprising because he was totally unoriginal except for being an Indian. As the interview goes on to say, he was strong, fast, and tough, but less so than the other X-Men.
In short, he was a dumb brute without redeeming value. About the only thing keeping him from embodying the savage stereotype was the lack of a weapon: a tomahawk or knife. In recent comics his brother Warpath has remedied this, making him a true savage.
For more on the subject, see Thunderbird in the Comics.