"He won't go in a carrier, he throws up in the car, he barks loudly at other dogs, he pees in the aisles, I can't carry him with packages in my arms, he gets tangled in his harness, people want to (gasp) touch him, I'm afraid he's going to get stepped on and basically it's just not a fun experience for me."
If my dogs behaved the same way, YES I'd rather leave them at home too!
It's no fun at that point.