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is there any reason why you need trained marksmen to shoot foxes but not rabbits?
The most efficient way I've heard of to reduce a rabbit population (short of myxomatosis) is lamping i.e., on the back of a landrover with a big spotlight and some people with shotguns. Rabbits are small enough that a shotgun will usually kill them quickly, or at least disable them enough to get to them and finish them off by hand.
Foxes, as I understand it, are tougher than that. You need pretty heavy shot in a shotgun to kill them, which most people don't carry round with them (which makes spontaneously shooting them if you're out for edible stuff unlikely). As a result you'd usually use a rifle to kill them. Rifle shooting needs tighter control and more training as the bullets carry further (shotgun pellets are ineffective above a couple of hundred yards).
I've never found the population control argument that convincing; have fox populations exploded since the hunting ban? As to shooting, is there any reason why you need trained marksmen to shoot foxes but not rabbits?
I can see there's an appeal to thundering around the countryside in a group - I quite like to do the same on a bike - but I don't see why that urge can't be fulfilled by point-to-points and drag hunting.