"Waarom vraag je dat?"
Translation:Why do you ask that?
That's okay! I'll try to answer them :)
First of all: Daaraan is an adverb, dat is a demonstrative pronoun. Secondly: 'twijfelen' only goes with daaraan (waarom twijfel je daaraan? = why do you question that?) and daarover (waarom twijfel je daarover?= why are you doubting/worrying about that?). These are the only two options.
'Waarom twijfel je aan dat?' is wrong. The only other option beside there two are 'aan hem/haar/hen', so to doubt a person.
F.e.: Waarom twijfel je aan haar/hem/hen? Why do you doubt her/him/them?
Sorry if my English grammar isn't right, I'm not sure sometimes, haha.