(They're also pretty heavy for anything but short distances and not always in great condition. And at least in Berlin where I lived you can get your own bike for $50 or so, which I had. But I still like the idea.)
If you buy a bike you lose some flexibility. With bike sharing I can take the bus to work, take a bike to my meeting and then decide whether to take the bus or bike home depending on the weather and my plans. I can also do things like take the bus into town and then take the bike from the bus stop to the place I'm going, or bike into town and take the bus home with all my shopping.
I live in a crowded European capital city (Bucharest) and one of the big reasons for me not buying a bike is that I don't have enough available place. I personally live in an one-bedroom apartment (before that I used to live in a studio) and yes, I could probably fit a bike somewhere around the place but that would be pretty inconvenient. I also live on the 8th floor and a regular bike doesn't fit in my building's elevator, so that would mean me having to carry it 8 floors up and down each time I wanted to ride it.
My gf does have a bicycle but for the reasons I mentioned above she decided to keep it at her office, which is at walking distance from where we currently live (about 10-15 minutes).