I would prefer shopping online to shopping in a department store 请问为什么是to doing?

因为这是 固定搭配：
prefer doing sth to doing sth
意思是：宁愿……而不愿……，比起……更愿意……

I would prefer shopping online to shopping in a department store
意思是：我宁愿网上购物而不愿意在商场购物。

这是一个惯用表达。to在这里是介词，介词后面如果是动词要用ing形式。

1.prefer doing sth to doing sth
2.prefer A to B (AB皆为名词)
3.prefer to do A(没有比较,只做一件事的就用这个）=would rather do A
4.prefer to doing A rather than doing B