This left-handed bias is an inherent asymmetry in nature and plays a crucial role in particle physics. In that case why should Nature have a left handed bais?/
Well, if you replace the electron with a positron and the proton with its anti-particle, you will find a right-handed bias. So, what you are asking is; why is the Universe made of matter and not of anti-matter.
This is not known. What is known is that electromagnetic and strong interactions don't show any such bias, while the weak interactions show a full bias: Particles that have weak interactions are only left-handed and never right-handed. The reason for this isn't known, however.
It's described within the framework of particle physics, but has non-trivial implications, also, for biology-where, in fact, this bias was first dixcovered by Louis Pasteur.