Number of MHCs in neurons
Antigen presentation by MHC will induce a cytotoxic response by the immune system, which is usually a good thing in the body since most cells can just divide and replicate again.  Neurons, however, are particularly ineffective at regenerating from such an attack, and are not easy to come by; they are also rather important!  Better not to risk it, eh?

That being said, neuronal expression of MHC is actually a pretty complex case, and this open-access article is a good start down the rabbit hole (see also here, here, and here if you have access).