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: 
First it's utterly inappropriate for that to be said. It is prejudicial, confrontational, insults their bosses decision making process and just avoids the specifics of whatever task they were working on. Remember, work is a job. And a job encompasses tasks. And most of the time if you are upset at a colleague you might just be upset at the task. 

That said, about 25 years ago if you did not have a computer science, general science or math degree and attempted to work in the computer field, you might get a basic I.T. job but that was it. Without a real computer science degree your career was limited in many countries and might not even be an optional requirement in others.

Nowadays—in most countries—computer science degrees matter but experience and proven skills level the playing field. For example 25 years ago you would have never seen computer science job listings that say a degree or equivalent work experience is required. Nowadays, work hard enough, learn on your own and prove your skills and you will be considered to be on par with those who have deeper formal training.

This is mainly due to home computers being more commonplace, the rise of the Internet and shared knowledge as well as technology being so widespread in the non-tech world there are tons more opportunities.

So if a colleague is ripping someone apart over a task and they attack based on their educational background, that is just violent, abusive, petty nonsense. How to handle depends on many factors but if this mentality is casually accepted in the office culture, it might be worth rethinking what kind of future one might have in such a non-cooperative environment.
It's not a nice thing to use in an argument, but all is fair in love and war and arguments. Depends on the actual university in question as well. If someone started citing their masters degree from the National University of Samoa, I'd probably start laughing.

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The best way to react if you want to remain professional is to tell them that university is irrelevant to the issue, and ask them to prove that they are correct. To me a uni degree means very little compared to practical experience. My reaction would be to ask them to cut the crap and show me their solution and then honestly appraise it to see if it's better than mine.