"Sin" is the possessive pronoun used for the third person singular or plural when the object is owned by the subject, regardless of the gender or number of the subject. In English that would mean "his/her/its/their own". Since in Swedish they have this specific pronoun, if you use "hennes" that would mean that she is selling someone else's dog (some other woman's dog).
I suggest you read the Tips and Notes before you do the lessons. They are very enlightening.