My husband and I have this "discussion" a little more often than we should. (Since by "discussion" I mean of course "heated argument".) Actually he has a point, our car is so old and we are >25 (by more than a few years now) with good records, it is paid off, so liability insurance is pretty low. Bikes need a lot of accessories that cars don't. I'm not sure that I can argue that I eat more because of bicycling, because I still have sufficient stored to fuel quite a few miles.
I conservatively calculate ~500 miles per pound of fat. So I could bike 10,000 miles on my stored fuel.
On the other hand it is an old car and invariably both the car and at least one bike seem to need repaired at the same time. The car always costs 10X as much as the bike to repair.
But then we end up using the car for things because of the bike. Like the trip to Columbia last week so I could ride on the Katy Trail with the Long Road Home Projects (vets biking Washington State to Washington DC).
The bike needs a lot of accessories and we don't have any accessories for the car. There's always something I want for my bike, or more often (and expensively) clothes.
The health costs can't really be calculated on an individual basis. My health care costs are much higher than my husband's. He doesn't bike (or exercise). Would my health care be even higher if I didn't bike? It's hard to say. The impact of bicycling on health costs is better calculated on a population level than an individual.
If you assume a gym membership in lieu of bicycling, that does increase the cost of driving.
Like diet & exercise, money is individual & complex. Probably most people would save money by using active transportation for most of their short trips. But not everyone. If you have a long commute, a bike ride of 45 minutes or more, you could easily spend that money saved on food & gear. There are lots of reasons why bicycling might not be cheaper for someone.
2009 Trek 7.2FX WSD, brooks Champion Flyer S, commuter bike