My question is why Chlorine does not undergo hybridis(z)ation as well? Supposedly, each Chlorine atom should undergo sp3 hybridis(z)ation to produce 4 sp3 hybrid orbitals, one of which is shared with the sp2 hybrid orbital of Boron atom. So, 3 sp3 hybrid orbitals from 3 Chlorine atoms share 6 electrons with 3 sp2 hybrid orbitals from Boron atom.
Why would it? Do you believe this configuration would be more stable?? If chlorine shares an electron with boron then it has a full sublevel. Regardless the other the accepted theory.