This problem exists in all Civ games. If your city has no bonus food resources, everyone is basically supporting themselves. When you move someone to a mountain or to be an entertainer, growth is dropped to zero.
What I want to know is how the elite civ players handle early growth? (before you get tech to allow 3 food per square)
I'm not an elite player but this is why you need to pick your settlement location well. Do you want high food early on or want more production/trade? Personally, I locate my cities near rivers or lakes so that I can irrigate stuff. If it suits your strategy, you can go for the granery.