I have a cat that doesn't like being carried. She was a stray we rescued from our back yard where she'd taken up residence under our shed. She's a very friendly cat, but really didn't like being carried. I accepted that. At first. And then, a couple weeks ago, I thought that I could desensitize her to being carried simply by carrying her to her favorite treats. So now, every so often, I'll pick her up and carry her around the house, stopping at a random site, and pulling out her treats. She adores treats, so after doing this a handful of times, she's already begun to tolerate being carried. My guess is that in no time, she'll look forward to it and I can reduce the treats to every once in a while. It's a simple training technique I've used in the past, but at the time, didn't realize what I was doing. You see, I was teaching a very smart cat how to shake hands. He learned it in no time, but he didn't like it. Not at first. He would literally growl when I took his paw, only tolerating it because he knew it would result in a treat. So he'd growl while I shook his paw and within seconds, pull it out of my hand. I'd give him his treat and try again. This went on for about two weeks, and then, suddenly the growls were replaced with purrs, and he stopped pulling away. From then on, touching his paws wasn't a problem, which made clipping his nails a whole lot easier, too!
I totally believe that training a cat brings you closer!