Yet Bootsrap's version requirements are perfectly reasonable...
1. jQuery 1.9 is obsolete, and you will have trouble with many newer browsers in any case. In any environment where browsers change constantly, you cannot expect old libraries to continue to work forever with new browsers. It's not the same as that old PC sitting in the corner running you shop inventory on MS-DOS 1.0! ("It just works, leave it alone...") Nor should you expect very old libraries to continue to work with newer ones, as new libraries will drop support for older ones.
2. jQuery 3.x is very, very new, and has changed in some ways that are not backward-compatible with previous versions. If you are going to be a pioneer, you cannot expect everything to work with it. Certainly not other libraries (such as Bootstrap 3.x) which pre-date it! Bootstrap was proactive in building-in a prohibition around this. If you are going to use 3.x at this point, you need to pick and choose third-party libraries that work with it, or be willing to pitch-in and fix them.
MOST developers at this point should probably be using jQuery 1.11.3 or 2.1.4 in production. It would be smart to test with 3.x though and be aware of issues and watchful of updates to third-party libraries that you can't do without.
I'd imagine Bootstrap 4 will support jQuery 3.x.
You go lucky that the part of Bootstrap you want to use (apparently) works once the proactive prohibition is removed. It may be that not all features work correctly, though. Other Bootstrap widgets may or may not work correctly.
BTW, when you post problems here, please provide more information than "doesn't work". You could have saved a lot of time by mentioning that you got a message that it won't work with certain jQuery versions! Reading your post, anyone would have thought that it was your assessment that it "doesn't work", but you didn't say at all in what way it "doesn't work".