Why does matter-antimatter asymmetry only refer to baryon asymmetry? Why is the matter-antimatter asymmetry of the Universe quantified by the baryon asymmetry,
$$Y_B=\frac{n_B-n_{\bar{B}}}{s}$$
i.e., the difference in the number densities of baryons $n_B$ and antibaryons $n_{\bar{B}}$ normalized w.r.t the entropy density $s$. What about other matter-antimatter asymmetries such as difference in the number of leptons and anti-leptons?
 A: People do consider the lepton asymmetry, it plays an important role in Leptogenesis. This is the idea that the baryon asymmetry was "born" as a lepton asymmetry, which was transferred to the baryon sector during the EW phase transition. 
Having said this, the baryon asymmetry is certainly discussed more often. This is because 1) we don't know what the lepton asymmetry is today, because we cannot determine the composition of the neutrino background, 2) we are made of baryons (and some leptons, which come along for the ride), so we would not exist without a baryon asymmetry (but we could conceivably exist without a lepton asymmetry).  
A: It is an experimental fact that we live in a baryon dominated universe.
If baryons and antibaryons were symmetric, we would expect to see an observational signature of that.
We know that the solar system is baryon dominated, starting that we landed on the moon, and now sent earth stuff to mars, and no explosions happened. Cosmic rays from the sun  and the galaxy are predominantly baryonic.
There is no signal of annihilation of baryons in the space between galaxies that would indicate an antibaryon galaxy. Proton antiproton annihilations produce predominantly pions and pi0 decays should be detected in gamma ray spectra coming from that region.
Thus one concentrates on baryon asymmetry, which is a problem, because the standard model of physics has everything symmetric except for very small CP violations which introduce baryon asymmetry but not in the large effect that observations show. It is one of the main problems of particle physics in trying to extend the standard model.
from the link:

There may also be a non-zero CP-violating phase in the neutrino mixing matrix, but this is currently unmeasured

In any case the enormous observed asymmetry between baryons and antibaryons in our observatble universe is what creates the problem.
