Okay, I can hear you saying, "Why would anyone want to pet a goat?" and I have to say that you have some logic on your side.
But it's surprisingly satisfying. Emma, the female Boer goat on the left, likes to be petted. She doesn't know why she likes it, and she's a little embarrassed about it, so she tends to just put herself in a position where if you happened to want to stroke her back, she's facing away from you and can pretend like she doesn't know it's happening. She stands very still while you're doing it, and you can just FEEL her enjoyment...and her puzzlement. Her back is surprisingly bony, considering that she's a little on the...overstuffed...side. (I have no room to talk in this department; I'm just reporting fact.) Her ears are really soft, but those are off limits. Only the back.
Arlene, the middle goat, sees no reason why you should touch her. Feed her, yes. Feed her all you want. Just don't touch.
Little Ben, the baby, is clueless about it all. He's nervous about being touched, but will tolerate it. We would like to do more of it because pretty soon he's going to be a billy goat with all kinds of goat testosterone coursing through his system, and just like a teenage boy, he's going to be butting heads with us, just a little more literally.
They each have a unique personality, and they're really a lot of fun. It's sobering to think that they were bred to be meat goats.
Lots of reasons here to become a vegetarian. Someday. (Do chickens have personalities?)