There are some good hypotheses about why the matter antimatter asymmetry exists.
This page explains a few of them. There's quite a large field of physics studying 'CP invariance' which is (brutally oversimplified) the assumption that antimatter can mimic matter and - in practice - there is no way to even tell the difference between the two when we make certain mirror image transformations (time reversal, etc).
As for my personal (and generally unfounded) belief, unless there is an unexpected breakthrough in some of these experiments, the antimatter / matter problem is really easy to explain away with the 'finely tuned universe' idea. It is somewhat maligned and cannot be considered a theory because it makes no predictions, but the philosophical foundation is fairly sound. Essentially, universes are formed and naturally selected in a darwinian process - those without antimatter/matter imbalance simply annihilate all matter and never allow the complexities of life/etc which could ever allow us to ask the question to begin with. This assumes you have a sort of multiverse-like view on how universes are created and how many of them there are.