Why would they cut down the forest to turn it into apartments? It's more economical to bulldoze existing single-family homes and do it there. The roads are already built, you'd just need to upgrade utilities and so on. There are people living in those single-family homes who would gladly take the opportunity to sell their land for higher than market value but are prevented from doing so.

It's more common for forests to be cut down because dense housing is illegal, so cities have to keep expanding outwards.