There is a difference between understanding someone and agreeing with them, which will become a sticking point in arguments when one person believes their opinion is a fact. We're likely to fight when I try to say that I understand you, but I disagree, if you think understanding and agreement are the same. If both sides have differing opinions masquerading as facts, neither side will budge, no ground will be gained or lost, and a very large amount of shouting will go on.
This is how a lot of internet flame wars start and how they continue. It is critical to clearly express that you understand your opponent's position, including the underlying assumptions, before stating your own position along with its assumptions.
Mokalus of Borg
PS - In the end, debating is about assumptions.
PPS - I like to start by assuming I am right.