The most important reason for animals _____ is the part that humans have _____.

选A
die out是"灭种"，die away 和die down都要"逐渐减弱直至消失"的意思，而die off是"相继死去"。
for sb./sth后面要加to do sth或者doing sth.
结合上面的意思和语法，只有A是正确答案。

D. to die down … played

to die down 不定式做定语修饰reason：动物灭绝的原因
play a part 是固定搭配，“扮演的角色”= “所起的作用”。
that humans have played 是定语从句，修饰part。

A. dying out … played

play the part
die out 灭绝

A,die out （灭绝）固定搭配

A
同一楼~