Question #76caf
1 Answer
A possible explanation was provided in 1967 by the Russian physicist Andrei Sakharov by invoking (among other things) an asymmetry in the interactions between elementary particles, known as "CP violation".
The C and P symmetries refer to the symmetry under exchange of particles and antiparticles (C) and the inversion of all three spatial axes (P). Although such a symmetry might seem natural, we now know that it is indeed violated.
The full explanation is extremely complicated. It also requires interactions that violate the conservation of baryonic number and also a cosmological period of inflation that effectively freezes the asymmetric situation so produced - otherwise, as you say, annihilation returns us to zero baryon number.
I should mention that in a normal physics degree course this would probably not even be touched upon, save to say what said above.