Also, Lela, some unsolicited advice - your profile says we're in the same city, but your time zone is an hour behind mine. Not sure why that is, you might want to check that out. Your rate is low and you call it out in your profile overview - it's practically an invitation for scammers. You certainly have the freedom to present yourself however you think is best, but that sort of callout in an overview ("I'm new, my rates are low") often results in a bad outcome. You're new here, but it doesn't mean you should sell yourself short or open yourself up to people who would exploit that.
@Lela G wrote:
I am just wondering, did they do this because I am new? Or does this happen to experienced freelancers as well?
It can happen to anyone, but sometimes when you're new clients feel like they have more leverage. They know that new freelancers are eager to get started, and also may not be sure what the norm is here or have a solid grasp of the TOS and user agreement, so some feel like they can get away with more with a new user.
You handled the situation perfectly, and if the client wanders off when you assert fair terms, you have lost nothing--that was not a client you wanted to work with, and that initial problem would not have been the only one you faced in the relationship.