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You might be thinking about AC power. In your house, AC power is grounded. Forget about that. DC power simply has two leads, one positive (power) and one negative (ground). Both are required for any DC device to do work. Your switch's job is to send positive and negative through those two wires, reversable.
And ditto what the other guy said. Do not plug this your antenna into a wall outlet. (kaboom!)
ac power in your house is grounded to work correctly, true, but there's still two wires that go to an outlet, and both have to be hooked up for the circuit to be complete and so it will work. Just like the dc circuit you're describing.
my question for OP is, what are you going to have that antenna doing in your coop? I wouldn't think it would be strong enough to raise a pop door, very curious