Why does China spend so much on agricultural/farming subsidies?
The first thing that comes to mind is food security. China has a large population to feed and does not want to depend on foreign nations for its food. 

A (speculative)  second reason may be prevention of domestic unrest. The largest share of China's population still lives in rural areas, and by supporting farmers they may silence protests. 

A recent article analysing the drivers of China's agricultural policies by Lopez et al., including the fairly recent shift from taxes to subsidies can be found here: 
https://www.sciencedirect.com/science/article/pii/S0305750X1630211X