Originally, I thought it made perfect sense for China to have no diplomatic relations with a small Catholic nation like the Holy See. However, I looked at a map that showed me that many countries with little to no Catholic population that aren't part of the Western hemisphere have diplomatic ties to the Vatican (like Japan, India, and Vietnam).
Also, China seems to have a goal of expanding its influence as a nation in other parts of the globe, something that relations with the Vatican would potentially help the Chinese Communist Party accomplish. So with that said, I want to know why the Vatican and China have no diplomatic ties with one another.