Well all disagreements are two party events, but if one person makes the first move, then the other disagrees I guess.

Each time money flows from one side of the channel to the other, there is a possibility of a disagreement. That said, until both parties agree and have signed transactions backing that agreement, nothing has officially happened.

So let's say, you want to update the channel, 500 sats from me to you. I get your request, I disagree. My node is handling everything in an automated fashion and really it disagreed because something about your request was not following the expected rules of engagement.

Instead of "negotiating", it just decides to break the connection ASAP and broadcasts the latest transaction it knows that your node also agreed with. Since the nodes never agreed on this new balance change, what is broadcast to the network IS the last agreed balance.

Also, if this dispute was part of a chain for someone to else's payment, that person's payment aborts and their wallet tries again finding a different route.