Question: I just witnessed an incident at my company where one of my colleagues accused another colleague and his arguments were based on the University he graduated from.

Is it correct to engage in such desperate arguments based on studies? The colleague who was judged is smart and even if he didn’t graduate from a computer science department he has a lot of knowledge in programming and 5+ years of experience in this field.

I’m asking because I also didn’t graduate a computer science university and I would like to know how to correctly react when someone brings such arguments.

Answer: 
Definitely not an appropriate argument. It's like saying "I'm right because I'm older." If you are at the receiving end of this, keep asking "why." If someone wants to claim superior knowledge based on whatever, he/she has the privilege of explaining the reasoning. Which brings the discussion back to facts. Something that is appropriate to argue based on.
It is not something that is typically appropriate but it kind of depends on the context. 

If it is was about syntax or stuff you can learn with practice then no. 

Let's say is was about a compiler design where if you have not been through the formal theory is not something you would readily pick up then maybe. But need to deliver with tact. 

Let's say you were at an accident scene and practicing bad (harmful) first aid and I was a Dr. To shut you down and get on with business I would say "Where did you go to med school?"