The consequences of deforestation are rarely anticipated, and when they do take place, are not always linked to the loss of forests. Resource shortages do not always result in reforestation efforts, particularly when living space is in high demand. There are always new regions to exploit, and the market is quick to make this exploitation attractive to the local users in new areas. The nations most aware of the effects of deforestation are the industrialized, literate countries whose forest exploitation enabled them to achieve economic success. These nations are often able to lower their need for wood through substitutions, and in the case of the US and Japan, succeeded in reforesting with some success.
Humans appear to be outside of the natural equilibrium cycles of the forest.
Sheer numbers seem like a good answer, but this is ludicrous if you think about animal and insect populations. Humans have the ability to transform a forest much faster than it can react. This is a better answer, but once again, an insect plague or a glacier can do the same thing. Perhaps humans are outside of equilibrium simply because we have the ability to modify the forest, the ability to realize that we are modifying it, an awareness of the passage of time and history, and no appreciation of the timescale on which equilibrium acts. Perhaps we are only able to identify the irruptive oscillations of sheep as an equilibrium process because we are not the ones eating all the grass and then dying off in droves.