There's a subtle difference here that's important to note. I don't think bikes belong on the road, but I do think bikes deserve roadspace. Saying "bikes do not belong on the road" could just as well mean "I don't want to sacrifice my car space for bike space". That being said, I think the hatred for bikes by motorists mainly exists because bikes are a liability to them. "These bikes infiltrate my road space!". With segregated lanes, it doesn't look like they use the road at all, and there's no direct threat to motorists. Who would be angry at bicyclists if you hardly even noticed them? Imagine pedestrians not having a sidewalk, and being forced to walk on the road between the cars. They shouldn't be on the road for obvious reasons. If you treat bikes simply as faster pedestrians, doesn't it make sense to also exclude them from the road? I've written about bikes before. There's more work to be done than just infrastructure: proper policies can do a lot to improve the hostile relation between cars and bikes.