How would you counter someone who thinks that a female is obligated to give every male who desires her a chance, even ones she has no interest in?

I would tell them to grow up. The world does not revolve around any one man's ego.

It's 2016.  Keep up with the times.  Everyone's on an equal playing field.  If a man decides that a women is obligated to give him sex, and does it without her consent, it's now considered as rape, and that is on about the same level, legally and ethically, as murder.  So if I were you, I would think before I spoke or acted.

And if a woman, or a person of any other gender, does the same thing, it is also considered rape and is also on the same legal and ethical level as murder.

I would counter them with a "WTF are you thinking?"

In what world is a woman obligated to give a man a chance? OBLIGATED?  Really? 

NO woman is obligated to do anything of the sort. 

Accepting attention is a choice .. Not an obligation .. Period.

I would ask them why they think a real man would be interested in a woman displaying obvious mental health issues with regard to relationships.

If I were a woman, I'd have better things to do.  Plus I would have "prequalifications" that would eliminate a large number of them.

And as a man, I would have no interest in any woman who made herself potentially available to all comers---does she not exercise any judgment in doing what she does.

First off, let me just say this: No one owes you a relationship, no one owes you a date, and no one owes you more than friendly compassion. However, I will say this:

Most women nowadays have an entire list of guys that are willing to date them. And yet, they complain about how they're single and can't find the right guy. None of these women try to TALK to these guys, or even give them a chance.

Do you have to give every guy who likes you a chance? No. Should you at least try dating a few of them and see what happens? Possibly.

I would counter it with "And this is why you are single."

However, I watch a programme called First Dates and I see plenty of women on there give up on really great men. They meet in a restaurant,  they have a great evening, they laugh, they share intimately, they hold their side of the conversation, they are generous and kind, but it ends with the woman saying "I didn't feel that passion, or that spark, or I didn't fancy him."

I didn't fancy my man either, I felt no spark, but he did stick around. I did feel comfortable with him, we shared a lot of difficult situations, he supported me, and with time he really grew on me, then one day I didn't want him to go, I felt I'd missed on an opportunity to kiss him. Then when he'd turn up I'd be excited, and have butterfly's in my stomach. I now fancy the pants off him, and I love him very much and am so grateful that he never passed me by because I was too busy focusing on things that were not important. He has taught me a great deal about myself, and how sometimes wrong ideas can get in the way of great opportunities.