I've recently gotten into riding and am discovering that it can be a pretty expensive hobby if you let it get away from you.
Yup!
He commutes on his bike rain or shine and claims that the savings in fuel and insurance alone are substantial.
Your friend is probably full of it if you ask for the actual numbers. Tires, oil, and fuel add up in a hurry, and the weekend few hundred mile rides you wouldn't do with a car eat the rest of the savings.
If you have a cheap bike (300cc or less if modern, 500-600cc if older), and only use it for required transportation, yes, it can be cheaper than a car. Modern stuff, and adding in the weekend rides? Nah.
That said, I don't care, and it's entirely worth it. We've got a fleet of motorcycles (my wife rides as well, and we recently bought a motorcycle with a sidecar so my daughter can come with us), I do most of the work myself, and it's something we value enough to keep doing.
However, I'll point out that as I get older, modern motorcycles are less interesting. Older, slower, clunkier stuff just puts a bigger grin on my face. The most fun motorcycle I have right now is the Ural - 2005, but substantially similar to a 1940s German BMW in a lot of ways. It's a gutless wonder, and I can safely describe the handling as "Doesn't go, doesn't stop, and doesn't turn" - at least compared to a modern bike. But it's hysterically fun to ride, you have to leave time for people to ask you questions about it at almost every stop you make, and it just puts a stupid grin on my face.
When I was younger, I commuted on a sport touring bike (I still have it, still ride it, but live in a less-twisty area now). Great fun.
But, seriously, you have to do most of the work yourself or maintenance costs eat you alive.