Jiraiya left for the purpose of watching over, but for basically anyone, notice that all the guys that are very talented and evil, tend to do bad things. And i may off a bit, but when you start to learn forbidden things, do things you shouldn't, or kill whole clans, I dont think the people there would really want you there anymore. Konoha isnt the only one, all villages have their bad pupils, take the Kisame other missing nins from other areas.

Tsu has her own reasons, as i wont spoil anything. But watch and you may soon find out.