Problem Solving In Systems

It's not the person that is the problem, but the system.

What does this mean?

It means "I am not the problem".

Is this denying personal responsibility?

It can mean that. But personal responsibility means solving the problem, and if the problem is part of the system, then it cannot be personally solved; the problem must be solved through and in the system!

It means most problems are the system.

A system is abstract, not a thing in itself. So an abstract system is the problem itself. The problem is not separate from the system. The system and the problem are one. If the system is the problem, there is no place for adversarial relations. 

On the other hand, if the problem is the person, then adversarial relations are required. Indeed, they are one's duty. But these are uncommon.