Hmmm ... normally when this topic comes up, we're referring to friendship in the biological sense of the word
Apply a bit of common sense: if your attempts at 'friendship' could possibly result in your student feeling uncomfortable in your presence and possibly leaving your flying school as a consequence, then you have pretty obviously just cost your employer a bunch of potential earnings and deemed yourself untrustworthy as well, and they would be quite within their rights to fire you.
There must be millions of people out there to strike up 'friendships' with, but not that many instructing jobs going for people who are known to make unwelcome advances on their students. And even if your student fancies you back, you can't escape the fact that it looks bloody unprofessional at best.