I never understood why the citizens of a city are against Genetrification. It improves not only the quality of an area, but can make you money if you own property there. Creating laws against it essentially keeps the poor, poor. On top of this, anyone with a little bit of succes and/or money leave.
It's just another example of politicians decreasing social mobility under the guise of helping the poor.
You are incorrect to assume that poor people own property in gentrifying neighborhoods. The dynamic is usually that low income renters get priced out of a neighborhood by high income renters.