How to proceed when advisor asks you to resign? This happened with a friend of mine and I am asking this question on his behalf.

My friend was recruited for a sponsored research project in the university and offered a part-time PhD along with that. He is currently completing his coursework (2nd semester) which is pretty exhaustive. He has been working pretty rigorously and one of his poster presentation was accepted in a reputed conference within 6 months of work.

Since the coursework in this semester was tough, he wasn't able to give any tangible output in terms of publications or concrete results. Now, suddenly he has been asked by his advisor to resign. This has come to him as a surprise since he was expecting some scolding as his guide is known for being arrogant (and he is very reputed researcher in the field).

He is unsure whether to leave PhD or how to proceed and convince his advisor.

I believe he is pretty new (1 year of coursework) to the domain and since the project is pure research, he does deserve a chance. But I am unsure of how one should proceed in such cases.

EDIT (based on queries in comment)

Part Time PhD: He was recruited as an employee for the project by the university. And also offered a PhD. The stipend comes from the project cost(funding agency) and not from university funds (as is the case for direct PhD recruits in my university).

Advisor being Arrogant: He is very knowledgeable and reputed but known for scolding students frequently.(Some faculty members also agree to this including my own advisor)
This is a difficult situation. Regardless of the facts of the matter, there appears to be have been a breakdown of trust/communication: either the advisor has been sending signals for a while that the person didn't pick up on, or the advisor is indeed pulling this out of the blue, which also signifies a breakdown of communication. 

Probably the best first thing to do is for the student to set up a meeting with the advisor to understand the advisor's reasons. It's possible that a face-to-face meeting might allow the advisor to express their underlying concerns in a more productive way that could lead to a concrete plan for activities. 

If that fails, or the advisor refuses to meet, the next person to involve is usually the chair of graduate studies at the department (or the equivalent). There is usually someone whose job is to oversee the graduate program and manage conflicts like this. They might be able to mediate a rapproachment between the advisor and student (or even find another advisor for the student). I've had to do this in the past when I served in this capacity. 

Bottom line: if the facts are as you outlined, then I think the student deserves a more reasonable explanation from the advisor as to why they're being terminated. Sadly though, in my experience  I've often found that students ignore signals being sent to them, and that advisors are unwilling/unable to give direct and clear feedback.