There's absolutely no reason why a guitar string can't be used for rabbit snares. In fact, I've seen rabbit snares which match the same thickness and quality as the guitar strings (these were illegal poacher traps that we dismantled).
All you need to catch a rabbit is a snare that the rabbit can get into but can't get out of. The bass strings would be much easier to prepare a snare with, while the treble ones might be a bit more difficult to work with to prepare the snare (more slippery and less malleable). Apart from that, no other reason why they couldn't be used.
As to why he doesn't use, it might depend on how good the rabbit population is in that area and how big they are too (guitar string is limited in length after all).