hello,我个人认为是句子缺少了成分,
The main argument would be the indispensable role animals play in various areas of our life.
改法1)The main argument would be the indispensable role animals +(that) play in various areas of our life.
改法2)The main argument would be the indispensable role animals play (playing) in various areas of our life.
不知道是否正确?