I have heard of the following reasons
They pray to Guan Yin (Goddess of Mercy) and the father Guan Yin was the "king of cows" and thus, it is a respect we show to deity Guan Yin
Buddhists respect cows for their contribution towards mankind, as they supply milk to man, and do all the hard work in the field
Gautama Buddha, the founder of Buddhism was born a Hindu, and thus abstinence from beef is a Hindu tradition that naturally goes to China hand-in-hand with Buddhism
However, based on my knowledge, beef is widely eaten in countries like Japan, Korea, China, Taiwan, Hong Kong, and Vietnam. Also, I would like to know if there's anything to do with the difference between Theravada and Mahayana branches. Which might explain beef's prevalence in the above mentioned countries.
I am not aware of beef being specifically forbidden in Buddhism, maybe in Hinduism ?
Some Buddhists are vegetarian (for example in China) in which case they don't eat any meat.