Why isn't wood a fossil fuel?

Fossilized wood, also known as petrified wood is more akin to stone than that of coal or the original wood, filled with mostly silicates such as quartz. As such it is no longer technically would and hence it will not burn.

A fossil fuel takes centuries of decomposition and compression and is mostly carbon or hydrocarbons.

Wood however will usually not be allowed to grow even as long as a single century before it is harvested. Also wood is not nearly at the right concentration of carbon to be a viable fossil fuel.

Finally, although you would not think it, burning wood is technically environmentally friendly, or at least carbon neutral. For fossil fuels, the process takes too long to match consumption and is finite. Wood upon burning, technically only gives off enough carbon dioxide to be absorbed by the other trees aiding in their growth and as such, allowing them to absorb more CO2. Obviously on the scale of a forest fire or that of the energy industry, the balance is overexploited but even still you would be more enviro concious if you were to burn wood over fossil fuels, which are full of other elements like sulphur.

I may have gone off at a tangent but I hope this answer helps.