Very nice post. I have two (minor) remarks.
But matter also has an equal but opposite twin called antimatter. So we have antiquarks, antineutrinos, antielectron(they're called positrons) antimuons, etc.
Strictly speaking, neutrinos may be their own antiparticles. It is actually the case in most neutrino mass models.
So why haven't we been able to achieve all this? Well, the thing is producing antimatter isn't so easy. The Large Hadron Collider operated by CERN is able to cough out about 10 million protons per minute when fully operational. Now that probably sounds like a lot.
Now, concerning the LHC. This machine is not actually the one used to produce and study antimatter at CERN. There are other devices dedicated to this aim. The reason is that even if the LHC produces a lot of antiparticles, all of those will annihilate before we would have the time to say a word. However, their tracks in the detector are sufficient for the physics investigated at the LHC.
Oh, thank you very much for pointing those out. On your first remark, is that because neutrinos have no charges?
That is one of the conditions but not the only one. Actually, the point is that one needs to extend the Standard Model to get neutrino masses, and this extension comes with extra features. In many models, it turns out that we have more than 3 neutrinos (I am currently working on a class of supersymmetric realisations of these setups) and they are all their own antiparticles.