If you are getting to interview stage, then maybe you need to change that up. Be more confident, don't let client feel that they are "picking" you but the opposite - you are picking your client out of those who come. Someone going for a job interview's doesn't pick who offers them a space and they know that.

Can you explain what your interview process is?
Do you phone interview first to weed out unsuitable client's so those who come you are confident in wanting?
Have they seen your contract and policies in advance?
Is your space clean and tidy?
Bright and well cared for?
Are the toys the right age group?
Do you explain what a typical day in your care is?
Why are you answering personal questions vs showing them the door? If they can't respect boundaries now, they won't as client's so it's good when they show themselves as unsuitable.
With due respect - does your home look very Asian and perhaps that creates questions about how Westernised your program might be?
How many space you need fill? If it several, do your ads say that and make parents wonder why you have so many spaces? If so, just amend your ads to state you have openings and leave it without a number for them to question.