为何用不定式而不用现在分词?

有一读者问: 有这样一道选择题:

(1)He has saved every penny he could_________the poor girl.

A. to help B. helping

答案是A,为什么B不对?现在分词短语不也可表目的吗?

这里应选A,表目的,这是不定式的经常用法。有人确实认为下面两句中的swimming和fishing是现在分词,表目的:

(2)I'm going swimming this afternoon.

(3)He often goes fishing in the river.

但对这种看法是有异议的。如从历史语法的角度来看,这里的swimming和fishing并非现在分词,而是动名词,其前省去了介词on。