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IMO the point is changing the position of centre of mass of the whole system (swing + kid mass) with respect to the hinge so to let gravity play its role and accelerate the swing. Then the conservation of angular momentum will do the rest.
Which is kinda how I tried to describe it. Kids can shift their COG quicker than swings can restore it.
Given a simple 2dof system, why would you expect to not be able to excite a resonant response, given control over one dof?