I'm not Mirzhan_Irkegulov, but my reaction to the two is very similar: both are correct, and in general no one has an obligation to have sex with anyone else and no one has an obligation to employ anyone else.
I'll guess that you're thinking about anti-discrimination laws, according to which in some circumstances an employer can get into trouble for not employing someone. But those are quite special circumstances that very rarely apply to sex (it might apply to prostitution, and I can kinda see a case for forbidding prostitutes to refuse clients on the basis of race etc., but also prostitution can be really dangerous and it's therefore probably better to say that prostitutes should have absolute discretion to refuse clients).
(The other obvious kind of case in which such obligations might exist is where a relationship is already in existence. You might reasonably be aggrieved if your spouse suddenly starts refusing to have sex, or if your employer fires you. But I don't think either side of this comparison is what anyone in the thread had in mind.)
Anyway. Apparently you consider that there should be harmony between one's answers to those questions. I'm pretty sure you don't think that employers should ever be obliged to employ particular employees. Do you think that women commonly have a duty to provide sex to men? In contexts other than existing long-term sexual relationships?
I'll guess that you're thinking about anti-discrimination laws, according to which in some circumstances an employer can get into trouble for not employing someone.
No, I'm thinking about the fact that politicians and pundits routinely talk about lowering unemployment, and this is universally agreed to be a desirable goal and not something creepy for implying that every worker 'deserves' a job, heck the "right to a job" is frequently listed in lists of "second generation human rights". Contrast this with the reaction advancedatheist got for suggesting men deserve a sexual relationship with women.
Speaking from personal experience, finding the right relationship can be HARD. I recently came across a rational take on finding relationship partners, much of which really resonated with my experiences:
http://waitbutwhy.com/2014/02/pick-life-partner.html
http://waitbutwhy.com/2014/02/pick-life-partner-part-2.html
(I'm still working my way through the Sequences, and lw has more than eight thousand articles with "relationship" in them. I'm not promising the linked articles include unique information)