1. They are only a net store of carbon while they're alive.
2. Because of that, you need to dedicate land to carbon-capture forest, indefinitely.
3. Burning fossil fuels for energy releases more and more carbon into the atmosphere.
Like, you get N tons of carbon captured out of a given land area. It's constant per area. So you would need to continually grow the amount of forested land just to follow the amount of carbon released by burning fossil fuels.
But: land is finite. The actual worldwide trend has been to deforest land, either for lumber, or slash-and-burn for subsistence farming in poor countries, or just to allow for population growth, or the large land area needed for wind and solar farms. We don't have a huge surplus of not-yet-forest land — can't grow trees in deserts.