Many good answers have been given already. One more is that many people understand it would be better for the environment and their own health if they biked instead of driving a car. Yet getting a car was one of the symbols of having the means for a good life. If you are able to let go of your car, it shows that you have held pointless things as important parts of your identity. You don’t want to have been a moron, do you?

So, you suppress the idea that you could be doing something else than what you are doing. And other people bicycling is kind of in-your-face. They show that you could have an alternative, and that causes a feeling of guilt in you. And that feeling of guilt is uncomfortable, and the people riding their bicycles are what have triggered that feeling. In other words: They have ruined your day by making you feel guilt. A completely self-created guilt, but an annoying feeling all the same. And then you hate everything that is connected to those people that keep ruining your days by the virtue of visibly existing.

This is not necessarily the reason for all of the people opposing bike infrastructure, but it is one of the important reasons for many.