Depending on how old they are, someone might have twinned a breaker because one was weak and they had some heavy load on the lines it was connected to. It may have been an accident where someone wired two together and didn't know what they were doing.

It's not code and not safe. I'd probably start by checking continuity between the two circuits (with power off) but unless you know how to do that, I'd not try.

All the receptacles and lights work with #17 on and #21 off. Everything works the same with #21 on and #17 off. Is that what you're saying? The circuit is somehow double wired or fed from two circuits. It's not right, but you may be able to cure it by removing the hot wire from one of the breakers. I think you shouldn't rely on advice you get here. You need an electrician. Could be a disaster waiting to happen. My son bought a house that had similar weird issues. We ended up re-wiring a few circuits. He's an electrical engineer, and he never did quite understand why or how it was working.

I'd imagine it's to deliver more amperage to that circuit, but that's a guess.

You have a multi-wire branch circuit. Very common. You can tell because each breaker is half as wide as normal.

Are they stacked together? You have to try everything in the room with each circuit on by itself

Sounds like two breakers wired in parallel together. Why this would ever happen is beyond me but as mentioned in the post you should get a licensed electrician, because you will never know for sure until they look at it.

The breaker that's supposed to be dedicated to your living room only turns on power to your living room? Does the other breaker turn on anything outside of your living room? For example, outside light or receptacles? Are any of the receptacles in your living room GFCI?