Why 長生き is 縁起でもないこと?

Why 美羽 is called 長生き - "縁起でもないこと"? Maybe she is one of the youngsters who doesn't want to live long?

俺：「せいぜい、長生きしてくれよ」
俺は優しく背中をなでた。
チロ（猫）：「うにゃぁ」
美羽：「うぅうん」
美羽が布団をはだけさせるようにして伸びをした。
美羽：「・・・・・・なに縁起でもないこと言ってるの？」
俺：「は？」
美羽：「長生き・・・・・・とか」
俺：「べつにそういうわけじゃないけどさ」
俺は苦笑した。
俺：「ただ、チロが拾われてきたときのことをちょっと思い出したから」

I could be wrong about this, but my guess is that the guy is telling (くれる in 命令形) チロ to live a long life and then 美羽 replies by saying something along the lines "why are you saying such a thing, it's bad luck/ill omen". Then he says that he didn't mean it like that, he just remembered some memories.
Edit: To make it more clear, him requesting/telling チロ to live as long as possible is considered to be a bad omen/bad luck.

That's my take on it at least.
There could be some other implications, but I don't know the rest of the context so it would be pure guesswork.
Note: You should wait for someone more knowledgeable to confirm my answer.

Do you know why in the theatre you never say "good luck" but "break a leg"?

Related vocabulary: 死亡フラグ.

I was going to mention the death flag thing, but wasn't 100% sure if this situation qualified.

I would guess the girl who said it was bad luck, at least, was thinking of it that way.

Also in the UK, never say "I hope it doesn't rain." Then it will definitely rain. It will probably rain either way, but no use in jinxing it.

Makes sense.
@killerinsidee , @nekojita thanks for help.