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: 
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?"
When faced with a foolish statement, I often prefer quips and sound bites to well reasoned arguments as most people are neither prepared nor interested in a well reasoned argument when they make a foolish statement. Here are a few to try.

"Those who can do. Those who can't teach. Those who can do neither study."

"So basically you're out of ideas and pounding the table?"

"Well, if that's what they do at then perhaps you should return to ."

Throw out a fictional institute of higher learning. Google for names. "You would never have made it at Faber College." Faber College was in "Animal House".

If you want a quip that is rooted in a well reasoned argument try, "Argumentum ad verecundiam". It means "Argument from authority", and it is one of many logical fallacies.

<https://en.wikipedia.org/wiki/List_of_fallacies>