The reason for a narcissist’s withholding in relationships is layered like an onion. Starting from the core, narcissists withhold love and affection because:
It makes them feel too vulnerable: Narcissists likely never received intimacy, warmth, touch or affection in childhood. They were ‘processed’ through their abusive parent’s ego-based false self. They were not seen for who they were, and they were not loved. In extreme cases, they were not even wanted. Their every breath was seen as an incursion on the parent’s existence. As a result, their True Self became a caustic wasteland devoid of warmth, and their false self became a protective layer. If you hold them, or acknowledge them, or seethem in the moment as they are, your warmth seeps into their True Self and reveals their repressed pain, anger and grief to them. So they recoil and pull away.
You’re not ‘high-grade’ supply: Narcissists want you to provide them with sex, services, attention and other forms of narcissistic supply. If you can do that and then leave them alone when they’ve had enough, then perfect. Love and affection are just a liability they don’t want to have to deal with (Refer to number 1). This especially holds true if you are not attractive, worldly, intelligent and ‘exalted’ enough for their liking. They classify people in a binary fashion: Low-grade supply, or high-grade supply. They rarely tolerate affection from low-grade supply, which creates a disgust response. However, with high-grade supply, they project perfection onto their target, and then affection becomes like a drug. They love it. If they always withheld love and affection, then you were probably low-grade supply to them.
Punishment: For high-grade supply, the narcissist will withhold affection when they are angry at you. Their rage, vulnerability and resentment are simply too much, and they pull away. On top of that, they get a self-righteous kick out of hurting their ‘perfect’ partner and bringing them down off their ‘high horse’.