They’re just being assholes. No seriously - this is all you need to know about their thought processes, because this is all they know about their thought processes.

Some people think cyclists don't belong on the road.

I've been riding a bike to work on and off for several years, and I pretty much also think cyclists don't belong on the road. The road is dangerous, far better to ride on sidewalks.

In the Northern Virginia suburbs where I live, there aren't a lot of people on the sidewalks. When I do pass a pedestrian, I slow down and give them a wide berth so they aren't startled. Sometimes I'll even ride into the street to give them more room, especially if they're walking a dog. And then, I get back on the sidewalk where my life isn't in the hands of aggressive or distracted drivers.

The issue with riding sidewalks, outside of pedestrians and it being outright illegal in most states, is driveways and curb cuts. At any reasonable cycling speed drivers will not see or react to you in time, because they're almost always focused on the road looking for passing auto traffic.

Far better in some cases, but far more illegal in others.

Since sidewalks in many places are rarely used by actual pedestrians it'd probably be better, and cheaper, to install paved bike paths instead.