As others have said above, much (but by no means all) of the reason for drivers and pedestrians hating cyclists is because of the behaviour of cyclists. The proportion of cyclists who break laws is way, way higher than that of cars. There should be no surprise that people complain, and feel scared of, cyclists more than cars, because cyclists (on average) are much more unpredictable than motorised vehicles.
Sure, better facilities for cyclists might help reduce law-breaking, but that doesn’t mean there’s currently an excuse for doing so.
In my experience offending cyclists defend their actions by saying it’s safer for them to do these things. But, no, 99% of the time, law-breaking cyclists are going through red lights and going on pavements because it’s easy for them and they don’t want to wait. I have a fifteen minute walk to work and every day I will see several cyclists pedalling the wrong way down one-way streets. There’s no safety reason for this, it’s simply laziness.
I think these cyclists don’t see rule-breaking is a problem because it’s just them, just a little old bike, and they don’t see themselves as part of a greater whole - the image of all cyclists. Sure, one light-hopping cyclist doesn’t make a huge difference, but its not just one, they’re not just alone. All of them together brings down the image of all cyclists and doesn’t help our cause.
Yes, “our” cause - I’ve been cycling my whole life and cycle much more often than I take public transport, never mind drive. Law-breaking cyclists make me angry because I don’t want to be tarred with the same brush as them. I want cyclists to be liked by other road users, but that’s not going to happen while the law-breaking continues on such a scale.