Is there a reason only certain lenses can be fitted with an extender? I'd really love to be able to fit the extender to some of my cheaper lenses.
The lens mounts have a specification over the maximum distances that elements can extend backwards - with EF-S lens, this is further back than on an EF lens. With an extender, which differs from extension tubes that don't contain any optical elemetns, the situation is reversed -- compatible lenses cannot go as far back as the normal EF lens specifications allow.
Adding an extender also has a big effect on the amount of light reaching the sensor and, more importantly, focusing systems, which can cause problems, and leads to unsupported configurations.
In either case, you may find you get away with it, but it may not be the same quality that you'd normally come to expect.
It's a physical limitation with the Canon 2xII, where the front element of the extender sticks out in front of the bayonet where your lens will fit. You may be able to find an alternative manufacturer's extender which has a different front-element design which will work with other lenses.
Even Canon's extenders can work with lenses you may not expect: the TS-E lenses for example can be usefully extended with the 2xII (I have tested only the 24mm TS-E mk1).