Because Beijing refused to do business with a country that formally recognized the ROC as a legitimate entity. The PRC considered Taiwan legally part of its territory (and still does so, officially) and it would be unacceptable for them to trade with and diplomatically associate with a country that was friendly with a renegade government like the ROC.

EDIT: to add more, the US was coming under increasing political pressure to accept Beijing as the legitimate Chinese government since it quite obviously held sway over nearly all Chinese territory. The US was eventually overruled by a vote of all the nations on which government would be keeping China's seat in the UNSC.