Why does my wood get used up so fast?

Wood in your warehouse (shown at the top of the screen) will be consumed by your cavalry troops, any amount over your current protection level will be slowly consumed. (wood stored in the bag / inventory is safe). Try to only fill the warehouse when you need to use it.

If you mean stored wood then you may be doing a lot of upgrades / research etc at the moment that needs wood. At different stages of your development you will need more or less wood and the other resources. Eventually you will end up with more.