It's just very easy to start with them. Rabbits in particular take very little space and you can feed them for free or nearly for free if you have access to a bit of forage. You can scale up or down very quickly (31 day gestation, so with just a bit of planning you can quadruple your meat production in a matter of months). Also I think that rabbits are actually the best converters of leaves into meat of nearly any animal besides fish.

However - beef or lamb/mutton is SO much better than rabbit! You just need more land, decent pasture (or be ready to supplement with hay for a while), good fences, and a watering system. Some folks want to work up to that, and many have larger animals as well as the smaller ones.