The co-pilot should not need to demand to fly (on average) every other leg.
Quite correct.
The blame, fault, or other could very well be put on either side of the fence, however. That the copilot doesn't fly may be the fault of the captain or copilot, but in any case, the copilot still has no right to every other leg.
Convention dictates that the operating load is shared, and in most cases, it is. One shouldn't be so fast as the bulk of the posters in this thread to assume that the copilot is owed something, or that the captain is at fault in the event a copilot isn't doing the flying.
I'd note too, that I'm familiar with some types of operations in which one may go the first year or two or more without hardly touching the controls, and this is perfectly acceptable in those types of situations.