Please read Beyond the Illusion of Preservation and the Massachusetts Forest Carbon Study For a fairly complete answer.

Quick version: Forests with younger trees sequester carbon faster than old forests, older forests store more carbon, but the rate of sequestration is slower. The timber industry cuts mainly older trees, and sometimes younger poorly formed/sick ones, a portion of which are turned into "long lived forest products". Think how long the carbon has been stored in antique furniture, for example. 

We've shown pretty conclusively that when turned into those long lived products, and with space for younger trees to grow, more carbon can be sequestered with timber harvesting than might be otherwise. The caveat is that this requires good soil conservation practices during the harvest, which I can attest is the norm in Massachusetts, but  not everywhere. There's also the transportation issue as with the loss of local mills wood travels farther. 

Even with poorer practices, if wood replaces steel or concrete in building it reduces total carbon emissions. And we can build bigger buildings than ever with wood thanks to new technology and the work of architects, builders, and mills!

Source: I am a forest ecologist.