Go over to backyard herds and you will see that it is not uncommon. It is for their own safety if they continuously stick their head through fences and get stuck.
Can't see the ad anymore but in this area, duct tape and a tobacco stick is pretty much the standard cure for a goat that's constantly getting its head stuck in fences. Might look goofy, but looking goofy is much preferred to having its face or hind-parts eaten off by dogs after getting hung up in a fence. We have one who hung herself up in a fence like three times in a day after having never done it before. She's one of VERY FEW that have horns here. Anyway, last time she did it, I gave her a little taste of what happens when she gets stuck in fences by basically getting to where I knew she couldn't see me and then doing scary things to her...picking her back feet up, immobilizing her back legs by squeezing her achilles, touching her belly, etc. Nothing painful or harmful, of course....just stuff that I know is nerve-racking for a goat. I made sure to do it until she started really struggling to get out of the fence and realizing that she was stuck there. Scared the crap out of her, and needless to say, she didn't like it AT ALL. Now before anyone goes "That's really mean!" -- you're right. She hasn't hung herself up in a fence since that day, though, and what you gotta understand is that there's not ALWAYS gonna be someone there to unhang her. She could die if she were to continue doing it.