Some cats can't get enough holding; others are skittish about it for pretty much all time, and there's no telling what might have happened to make them that way.
Our lovely little Kali, who died almost two years ago, was like that. She loved us, and just about everyone else she met, but when it came to being picked up and held, you did well if you had her for 30 seconds or longer. Picking her up to carry her someplace was fine. But there was very little "just holding her". It wasn't a fear issue -- put her down, and she'd stay right there to be petted till the cows came home. But she never liked being confined in people's hands for long.
DR Elmore's descriptions of Thatch reminded me exactly of that