"Can't" isn't quite accurate - what it really means is that the rate of metabolism is significantly slower. Dogs can (and will) eventually metabolize and eliminate theobromine, but the rate is slow enough that the compound can build to toxic levels quickly following ingestion.
In general, mammals are capable of metabolizing and/or eliminating nearly any foreign organic compound over a long enough timespan, thanks to the mechanisms of xenobiotic metabolism. The liver contains a large number of enzymes of the Cytochrome P450 (CYP) family, which are able to catalyze reactions with a wide variety of compounds as the first (and most critical) step of metabolism. These reactions typically make the compounds hydrophilic, making it possible for the kidneys to pick them up and eliminate them. However, different animals express the various CYP enzymes at different levels; some are much more effective at metabolizing certain compounds (e.g. theobromine) than others. So, if an animal lacks a certain CYP enzyme (or it is expressed at a very low level), they will also metabolize certain compounds much slower (other enzymes, which are less efficient, will have to do the job).
So, basically: dogs lack certain enzymes in their liver which means that they metabolize theobromine much slower than humans - but that doesn't mean they don't metabolize it at all.