Even something as simple as an oil change can go wrong. Drain plug broke and you need a new one? Or you forgot to put a gasket and it leaks and now all your oil is on the floor? Well, now you need a trip to the parts store, or order it and wait until parts get there.
In my case, it was a routine maintenance operation: changing brake fluid. I used a power bleeder, and at a third of the pressure specified on the manual, the reservoir ruptured. So now I needed a new reservoir. Parts store didn't have it, and it took 2 weeks to get there.
Hey, better this happen while you're wrenching than when you're zooming through the twisties and need to stop
Luckily that one was just a quick trip to the parts store to get the right fluid and reconnecting the line properly this time!
Often I'd invite a friend over while I did the work, keeps me company and that way they can be the backup vehicle (and I'd return the favour).
This is the other reason a lot of people will do their own motorbike maintenance - for a lot of people, the motorbike is the second vehicle.
It's also rare to order too many parts or tools. Rental tools are very useful, but many times as a car ages, you may need to order other parts.
Though I don't get this complaint; because there is often lead time at a mechanic's for the parts too; you still need a backup transportation plan for that situation. (And it's even more likely to effect you during a 9-5 if you your wrenching on weekends or weeknights)