Actually, they do.
You may have paid for them; you may have the bill of sale showing ownership; but they follow whoever feeds them.
My calves know my voice; and they know that when I say a certain phrase a certain way, there will be food. They've gotten out a few times and mingled into the neighbor's herd; but when I call them, they respond. Now, here's the kicker: the neighbor's calves know my voice, and that when I call, my calves will be fed, and they respond, too. Even if it's just mooing in frustration that they're not getting fed like my calves.
But they're not mine.