When tabby balks at being picked up, it could be as simple as how you lift her (or him) or/and how you hold him (or her) afterwards.
Tabby grabbing is a nicer way to say, "pussy grabbing." To your cat, it can be as invasive as sexual assault is to a person. One thing you always need to remember in handling a cat is that an angry sounding "meow," a hiss, or a growl is as valid as a human, "No!"
Grabbing a child by the scruff of the neck used to be something parents referred to as a type of discipline. These days it's called "abuse".
Likewise, never pick a cat up by the scruff of the neck except to save its life.
You may have seen mother cats use this tactic, but they do it with a soft mouth and their hold is nearer the kitten's shoulders than its neck. In addition, a kitten being moved by its mother is tiny. It weights next to nothing. Long before it has grown enough to be adoptable, it will be able to locomote on its own. Its mother will no longer need to pick it up by the scruff so she won't. You shouldn't either.
Cats pick up their kittens because they don't have hands to use. You do. Use both of your hands to pick up your cat in the same way that you would pick up a toddler. Then, when you hold your cat, remember that it is not a toddler.
Cats do not like to be cradled. A cat doesn't like his stomach (most vulnerable area) exposed unless he exposes it. Cats don’t enjoy belly rubs like dogs do. Your cat may appreciate the occasional chest rub, but only when she lies down and exposes her chest to you.
It could be the way you look at your cats that puts them off.
Looking at a cat wide-eyed is an aggressive taunt to a cat. When you look at your cat, narrow your eyes.
Try a slow blink, which is a sign of trust and (some think) affection. If the cat blinks back, he sees you as a friend.
Don’t just reach down and scoop your cat up. Introduce yourself. Before you pick Tabby up, scratch the top of her head, her jowls, or under her chin. This is your agreement to carry her scent and it feels good to your cat. If she walks away from you, let her go. Try again later. If the cat is liking it, she will let you know by rubbing harder against your fingers and/or purring.
Be patient. If you’ve been a Tabby Grabber, it may take some time for your cat to figure out that you’ve changed your ways.