The first thing you should do is ask questions. Clearly it is important to examine your relationship with your angry 'peer' to see whether there is anything in your history that might be relevant to the apparent problem. Most importantly, you should very gently and diplomatically try to find out your peer's interests and concerns. You need to find out whether you or a particular issue are the problem. You should also ask yourself what kind of long-term relationship is involved or is desired.
Information is the fundamental asset of negotiation.
You learn the most with your ears open and your mouth closed. Let me know what happens.