The sulking is a choice.
It is a weapon through which he wants to manipulate you.
He might want to have sex every day but no one is entitled to sex at all.
Lots of people may have desires that are not being fulfilled - be that for sex, sunshine, chocolate, power, uninterrupted sleep or some niche kink.
We may not choose to have that desire but we are able to choose how we respond to it not being fulfilled.
If his interest in you is reliant on having sex four or five times a week, then he is actually interested in you. Over a long period, even couples who both have high sex drives at the start may face periods where one person is unwilling or unable to have sex (eg, illness, chemo, recovering from a car crash etc, grief). Imagine having chemo and having a partner sulking because you weren't allowing him to penetrate you.
Don't tell yourself he wouldn't do that - cancer nurses will tell you that many relationships end when a woman is the one unwell as the men leave as they don't like not being the priority where as women rarely leave their unwell male partners.