Offsets -- considered indispensable to keeping cap-and-trade affordable -- are supposed to be "additional" reductions beyond what is legally required. But experience with offsets in Europe and California has shown that ensuring real "additionality" is not an achievable goal.
Suppose, for example, that a landowner is paid not to cut his forest so that it can continue capturing carbon dioxide from the atmosphere. Purchasing this offset allows owners of a coal-fired power plant to burn extra coal, above the cap.
But if the landowner wasn't planning to cut his forest, he just received a bonus for doing what he would have done anyway. Even if he was planning to cut his forest and doesn't, demand for wood isn't reduced. A different forest will be cut. Either way, there is no net reduction in production of greenhouse gases.
Here is a different example of "offset." A friend comes to me and says, "I want to have an affair, but if I did I would feel guilty about increasing marital discord in the world. So I want you to forego that affair your were "planning" to have. That way, the net number of affairs does not go up, and I will not feel guilty."