If you look at the electronic structure of Carbon, it has four unpaired electrons. Nitrogen meanwhile has 3 unpaired electrons and 2 paired electrons. So carbon will want to form four bonds which it does in the case of benzene. (Though in benzene three of the bonds are kind of inbetween due to aromatic nature of the molecule. But for our purposes, each of the carbon atoms in benzene has four bonds). With nitrogen, it only needs to make three bonds in order to have the 'full octet', and if it were in the same structure as carbon is in benzene, you'd have a heck of a lot of unpaired electrons. Those unpaired electrons would probably interfere with the bonding between the nitrogen atoms and would probably also be very attractive to positively charged substances. As a result, the bonds between the nitrogen atoms would probably be ripped apart by other species. So yes, I think stability is a very key issue here.