Wow! I didn't realize so many furbutts felt this way. In the the early days, Guinness would literally turn into a stubborn mule. We'd get ten feet from the front door when he does a dead stop and goes into a sit position. He would firmly plant his back legs while his front legs stiffly stretched out before him like he was bracing himself. Then he would pull his head back and lean back with all his weight. I mean seriously, if I were to give the leash a little slack, he would fall over backwards.
The following day I decided to get just as stubborn.

There we were, ten feet from the door again. It's raining and he's Mr. Mule. I just stood there holding the leash steady, telling myself, this is going to take however long it takes. I have my raincoat and he's getting wet. But eventually he moves forward and we walk to the spot where he does his business.
These days, I put on our rain gear, we run to the spot, he does his business, then we run home.