why are nose piercings considered unprofessional ?

Societal norms. As society changes, so does what is considered professional. And I'm not sure if they would be considered unprofessional, but they do not give the appearance of a professional. The same reason why people are expected to dress nicely especially when dealing with prospective clients. Dress has of coursed changes as society has changed. No long is every professional male expected to wear a suit and tie at all times in the office. This was once the norm and anything else would be considered unprofessional. Why? Again, no exact reason, just an expectation of appearance. 

Because- and be honest here- people who choose to have their noses pierced and present themselves to the world that way are doing it out of rebellion. Most employers do not want rebellious employees,

You're mutilating yourself to try to make yourself look good, you're not winning someone's respect through how you conduct your affairs. Your character and who you internally say more about you than your outer appearance and trying to draw attention to your outer appearance through extra things like piercings, tattoos, etc is rather a distraction to how really you should serve the public in retrospect. Body piercings are just not necessary. 

If you need an extra hole in your nose, It is because you obviously are too stupid to breathe with just two. It's like getting another leg because you are too dumb to walk or lost your leg or something- pure ignorance

Students in a school have to look like they are going to rise to high, responsible positions and therefore contribute generously to the school as good alumni.

It's a generational thing for sure.  Body manipulation, aside from conservative earrings, has been always been frowned upon in the business world.  Personally, I think nose piercings are ugly and disgusting, and therefore unprofessional.  By unprofessional, I mean they're no different than having a ear disc or tattoo on your forehead or a real bone in your hair.  (Yeah, I've seen that.)  There was a time not too long ago that even the wrong size or shaped earring was very unprofessional.  This type of free expression and body manipulation is something traditionally reserved for those not in the corporate or business world.  (Skaters, 'punks', low-life individuals with no future.  I see that changing, but it's still relevant.  

Add to this that if you represent the company.  Even if they don't overly care, their customers might.  You are the image of the company even if you are not customer facing.

I've seen this change quickly over the past 10 years though.  More and more the offices I'm in have young people with 'conservative' nose piercing.  Region matters as well, of course.

the perception of body modification (tattoos, piercings, ect) has changed pretty wildly after the millennial generation came through adulthood, they are way more acceptable now. older generations, the ones writing the rules, still associate them very strongly with movements like punk, which were anti-establishment.

nobody wants to deal with someone that has a booger encrusted ring flopping under their nose ..

I don't get it either. What is unprofessional about how you choose to express your personal style? 

Because most humans are not cattle.