As we have already discussed, the reason we have particles without anti-particles is because of CP violation. CP-violation caused slightly more particles to be produced in the big bang then anti-particles. Then all the anti-particles annihilated with a particle leaving only the excess of particles we observe today.
However, it takes 3 generations of quarks to have CP violation. CP violation is encoded in the CKM Matrix, a 3 by 3 matrix. (N=3 for 3 generations of quarks). You need a overall phase in the CKM matrix to have cp-violation. If there were less then 3 generations of quarks, say 2, then the new 2 by 2 CKM matrix would have no overall phase and hence no CP-violation.
It was not too long ago when scientists had not suspected there were three generations of quarks. If there weren’t, we would have no CP-violation and no matter. It would have all been annihilated with the equal abundance of anti-matter.
By the way, in case you don’t know, the CKM matrix people won the Nobel Prize in physics last year.