It wasn't just automakers, it was also the car owners. The first cars were owned by the 0.01%, and those sorts of people don't like being held responsible for mowing down smelly, dirty plebians.

So, they paid for cartoonists to draw cartoons that made pedestrians look like careless idiots, got their newspaper-owning friends to write editorials, the car companies joined in, and boom, jaywaying laws.