Cost is the main one, with flexibility of selecting your own hardware being second. If you are just getting started, and you want to keep costs low or you don't have enough demand to justify buying hardware or building data centers, the cloud is perfect. This is the Uhaul stage, where you only move once every few years, so it makes sense to rent.

As you grow you might find that you were starting and stopping servers all the time to match demand or for batch processes, but you keep 100 servers on all the time. Or it could be that you want specific hardware that the cloud providers don't have (e.g. a specific CPU or drive). It might make sense to move these to purchased hardware to keep costs low or get the exact hardware you need, but remember that you'll have to deal with buying new hardware when it gets old or fails, and buying additional hardware to scale. This is the touring band stage, where you buy a van instead of renting one.