Hmm... I wonder why. I mean, if the tuition subject is not
Mandarin, then it's not really necessary to insist on
'Chinese-speaking'. 
The female bit ... ok, if they have a daughter who's going to be
home alone, then they might have concerns with the gender of the
tutor, for safety reasons. Not saying that ALL male tutors are
dodgy, but sometimes, it's a risk the parents would rather not
take. Guess the parents are just being very vigilant.
How about asking your aunt, who's happy with the results you have
produced, to ask around and recommend you to the parents of your
cousins' classmates / schoolmates?
