1.B
despite是一个介词,其后加all her arguments做宾语,所以选项做后置定语修饰arguments；
on the contrary在句中只能做状语且单独使用,排除A；
in contrast一般不单独使用,构成短语in contrast to/with...,且其意思是“（和...）对比”,和句意不符,排除C；
to the contrary单独使用,即可做副词充当状语,也可做形容词充当定语,意思是“相反的/地”,且与句意相符,所以B为正解.
2.A
such即可做代词,也可做形容词,做代词时候可以单独使用,类似于名词,翻译为“这样的人/物/事情”；
so只能做副词,修饰形容词/副词做程度状语,不能单独充当句子成分.
而该句是一个明显的so/such...that...句型,选项在主句中单独充当表语,而后的that引导一个结果状语从句.
所以只能用代词such充当表语,而so不能单独充当句子成分,排除B.
3.C
定语从句,关系代词which代替先行词the professions,在句中充当介词for的宾语,且和for一起提前至定语从句句首.
即：for which they were trained
= they were trained for which
= they were trained for the professions
these/what都不能引导定语从句,排除BD；
表物的关系代词放在介词之后时,只能用which,不能用that,排除A.