Posner's discussion of carbon offsets is thorough, so I will concentrate on only a few issues. The main obstacles to a large reduction in the aggregate emission of carbon dioxide from any offset system are that the system is likely to affect only a small number of persons and companies that produce carbon emissions, and also that many alleged "offsets" have only a small net effect on emissions.
It is an impressive testimony to the power of the "green" movement that many consumers, and some companies responding to consumer pressure, are voluntarily seeking offsets for the carbon emissions from their diverse activities. Nevertheless, the carbon-offset movement still has only a tiny fraction of all consumers and companies worldwide. Even if the movement doubles or trebles in size, and even if the alleged offsets are real offsets, its overall effect on carbon emissions will remain quite small.
Of course, the numbers involved would multiply greatly if offsets for emissions became compulsory rather than voluntary. But then the carbon-offset system would be fundamentally no different from a carbon emission trading system of the cap and trade variety. Cap and trade systems, and any compulsory offset system, presumably would apply only to companies since enforcement and management of the system is much easier for the relatively small numbers of firms than with the hundreds of millions of consumers in the US alone.
The natural link between an offset system, whether compulsory or voluntary, and an emission trading system does dispose of the criticism that offsets are not desirable because they are like the indulgence system of the Middle Ages, In that system, sinners could purchase forgiveness for some of their sins without either having to repent, or having to agree not to sin anymore. Yes, an offset system does essentially involve buying the rights to pollute, but buying such rights helps get polluting into the hands of those businesses and consumers who get the most value from these rights. That is why the world has gravitated toward a cap and trade system rather than merely a cap system.
Another major problem with any carbon-offset system is that activities producing the so-called "offsets" may have happened anyway. For example, an initial and still popular type of carbon offset is to pay for the planting of trees in a reforestation project, particularly in the tropics. Forests help cool the atmosphere by storing carbon. It is quite difficult to determine whether any particular tree-planting program makes a net contribution to planting, rather than simply displacing other tree plantings that would have occurred anyway.
As one example, a country located in the tropics may have planned on a reforestation project for several reasons, including a reduction in the degree and rapidity of water runoffs during rainstorms. If a carbon-offset project began to plant trees in that forest, the country may cut back on its own efforts since these would be replaced by the tree plantings that serve as carbon offsets. TerraPass, an important company that sells carbon offsets, was accused of selling offsets in a methane recapturing project that allegedly would have happened without the TerraPass offsets (the company denied this claim; see the discussion in the Wikipedia article on "Carbon Offset").
In our complicated and interdependent global economic system, opportunities to create carbon offsets can be readily produced by both companies and governments without any significant affect on the scale of emissions. Mainly for this reason, but also because of the reluctance of most individuals to voluntarily pay significant costs for acting "green", a cap and trade system, despite its many flaws, is a far preferable direction to develop in order to cut down on carbon emissions.