They think of it as a zero-sum game

But it’s not.

The reason you need more lanes is because of a growing population using a fixed set of roadways. As you add protected bike lanes, more and more people opt for using a bicycle. This means fewer people on the road, negating the need for the extra roadway.

If you spend limited tax dollars on bike infrastructure, driving infrastructure will not receive necessary maintenance.

I’m not sure what you personally believe, but this is not true at all.