Cats have a range of personalities. Some cats love to be super affectionate with their owners and crave snuggle time. Other cats seem to value their own space and seem to just tolerate the presence of humans.
While some cats enjoy being held, others will squirm and go stiff the minute you pick them up. There are several reasons why your cat may not enjoy being held.
Lack of socialization as a kitten
The most common reason why a cat doesn’t enjoy being held is a lack of socialization. The window for acclimating a kitten to being held is actually quite short. The optimal time to socialize a kitten is from 2 to 7 weeks old.
Kittens that had a positive experience being held and cuddled during this window tend to be the cats that enjoy being held as adults. Older kittens can still be socialized when they are older and will be affectionate and friendly towards humans but may still retain a dislike of being held.
One study that looked at how well household cats accepted being carried by a stranger discovered that the more socialization a cat experienced as a kitten, the less likely the cat was to try to escape while being held. 
Your cat has trust issues
Being comfortable with being held by a human involves trust. Cats that don’t fully trust you will be less willing to be held. Being held can feel restrictive and threatening to some cats, especially ones that have been traumatized or abused in the past.
Your cat is busy
Your cat may simply not be in the mood to be held. It’s important to read the body language of your cat when you attempt to hold them. They may be in the middle of playing or wanting to go someplace quiet for a nap.
If your cat’s body is stiff when you pick them up or they are squirming to get away, gently put them back down for now. A flickering tail is also a sign that your cat’s annoyed with being held and wants to be put down. Your cat may even growl or hiss to indicate their irritation with being held.
A cat that’s content with being held will have a relaxed body.
Your cat is scared
As pet owners, we like to think of ourselves as the guardians of our little furry pets. Your cat’s instincts, however, is not to flee into your arms. A frightened cat wants to flee and find someplace dark and quiet to hide.
Your cat is sick or injured
If your cat is experiencing a sudden dislike of being held, they may be sick or injured. The natural instinct of a cat in distress is to hide. Cats tend to hide their pain so it won’t always be obvious that the cat is sick or injured.
If your cat’s suddenly repelled by being touched or held, check with your vet to make sure they don’t need medical attention.
Your cat just doesn’t like being held
Some cats will never enjoy being held, even ones that were properly socialized. Cats have different personalities and different ways they prefer to show affection. Some cats will only ever enjoy sitting near you while other cats want to constantly sit in your lap.
It’s important that you accept the terms of how your cat wants to show you affect. Read your cat’s body language to understand how and when they want to be affectionate.
Don’t try and force your cat to be held if it’s just not in their nature. You will only end up with a cat that’s distrustful and distant towards you.
 Lowe, S. E., & Bradshaw, J. W. (2002). Responses of pet cats to being held by an unfamiliar person, from weaning to three years of age. Anthrozoös, 15(1), 69-79. https://doi.org/10.2752/089279302786992702