So is "bierzesz" a verb that takes a genitive object, then? What would "why are you not taking the bags?" be?
Edit: Nevermind, just remembered the negative-genitive rule.
Well, they can be synonymous, but "purse" can also be more like a... women's wallet ;)
In the hints for "torby", it says both bag and handbag, but handbag is not an accepted answer ("You used the wrong word"). The Cambridge Dictionary translates handbag to "torebka", so I am guessing that "torba" is bigger than a handbag?
Personally I'd rather teach "torebka", it seems more common to me, while "torba" is indeed bigger - although one can have a big handbag, of course. Anyway, this sentence and any other with "torba" should accept "handbag". Added now.