Rabbits don't like to be picked up. You can see it when you start to lean down to pick up your bun, ready for some snuggles. Your arms make the first tiny moves to reach for Daffodil, and there she goes...off like a shot, under the couch or behind the tv. Now, you are pretty sure Daffodil does in fact find you to be a good friend. but she just doesn't seem to want to cuddle! What is up with that?
Time to think like a rabbit.
In fact, go ahead and close your eyes and imagine you are a rabbit in a beautiful meadow. Eating some leaves, enjoying your day. You see a shadow approaching...a big one! OMG run to safety! Danger, danger - a hawk is overhead!
Rabbits are small and low to the ground. They are also primary prey animals. So anything coming from above is a big threat, and their instinct is to race away. Even if they can see YOU are the thing coming from above, that instinct is so strong, and so ingrained, that they really can hardly help themselves.
Even the feeling of being picked up signals danger in their rabbity brains, since this is only something that happens when they are in the grasp of a predator. Yes, the may know that you won't harm them, but that knowledge is overridden.
There is genuine fear in this situation. Your rabbit may learn to accept being picked up, but down deep inside, in the most ancient recesses of the rabbit brain, chemicals are being released that cause physical responses to danger. Your rabbit will learn to "ignore" these, but even the calmest bun is indeed having a physiological response to being picked up.
So how can we avoid causing this kind of stress? Well that is super easy. Don't pick up your rabbit. No, seriously. There are ways to avoid the whole thing.
Provide ramp access in and out of any raised pen or crate. With a little reward system, your bun will soon learn to race right down that ramp for some play time, leaving the pen or crate free for cleaning or other chores.
If you need to pick you rabbit up for some grooming or a health check, you can train her to enter a carrier (or even just rabbit size box or basket), then move the rabbit in her "vehicle" to the table or couch or whatever.
Want a snuggle? Don't we all! If you are able, try getting down on the floor and allowing your rabbit to come to you. It may take a little patience, but they will learn to trust, and will scamper up on your lap. If you are unable to get down on the floor, try sitting on the couch and providing an easy way for your bun to jump up there with you. Either use the "get in the vehicle" method, or just encourage a good rabbity jump by providing some great smelling greens, herb mixes, or other little nom noms up there on the couch.
If you avoid the entire picking up scenario, your rabbit will learn to trust you more, and your relationship will deepen. Here's a little video for encouragement: