Rabbits don't being picked up, I think everyone in their heart knows this. However that doesn't mean they don't like your company or being touched. I think embracing how your rabbit prefers to socialise can actually make your bunny closer to you - my mini lop Fidget is a lot calmer and affectionate these days after I adjusted the way I spend time with her. Rabbits are not dogs: firstly, they are prey animals so they may fear you. And despite living in communities, rabbits quite like their own space. So combining this, what I do with Fidget is make sure that touching me is always her choice. I spend time with her in a large run or on my veranda where she has space to run around and explore, some food to nibble on, places to hide if she's upset. I sit, usually reading a book for a few hours. I talk to her often so that she is able to notice my presence and emotion. she will come up to me, head bop me, lick me, sometimes even climb onto me and then go do her own thing. Sometimes we will share the couch while I watch tv, and she will thump when she needs the toilet - I didn't train her, she just figured out how to communicate her needs. It is actually more fulfilling than when I tried to force her to cuddle me.
Obviously, touching and holding them helps us as humans - it's how we show affection and petting animals can do wonders for stress levels, blood pressure and health. But there's more to it that that - your rabbit needs to tolerate being held so that you can groom them, clip their claws, check their teeth, eyes and weight. So making sure holding you bunny in away that makes them feel comfortable is still important. When you approach them, make sure it is at their eye level, and that they can sniff your hand or look at you before hand. Then pick them up, gently, and put them with their feet to your chest ( the manoeuvre you may have been taught, with one hand on butt and one of their chest is better for larger animals - ground dwelling rabbits much prefer the sensation of having their feet grounded). Take them to where you can sit, and let them sit on your lap. Put them in a trance by stroking continuously from nose to forehead. If you need to flip them over, make sure you have them on a soft but solid surface, and make sure you trance them again while they're on their back because they really don't like it. Then you can check or clip claws, teeth, and give them a general health check. I do this once a week with Fidget - she give a big foot stamp afterwards to tell me that she's not amused, but then I gives her a nose rub and she seemed to forget all about it.