Thanks for the update Harveybunny! It’s great that you are doing your utmost to not discomfort your rabbit or do anything that your rabbit may dislike.
Picking up a rabbit is, by default, something you should avoid doing because as you mention, many rabbits do not like it at all; however, there are times when you need to pick up a rabbit for transportation, safety, or medical reasons. In these cases, as long as you’re doing it in a way that is not harming your rabbit, I think it’s acceptable. It is good that your rabbit felt secure when you were holding him.
A rabbit has its own mind and intentions. Lets say someone randomly opens your front door and leaves it open. Just because it’s open does not mean you want to necessarily leave. Maybe you want to stay in your house at the moment, or maybe there’s not really much out of your house that you’d want to do; however, going out of the house is important for exercise and general mental stimulation! So, what to do?
I would encourage feeding him outside his cage to get him comfortable with leaving and being in the new living room environment. It may look very new to him, have smells he’s not accustomed to, and maybe he hears noises you can’t. He feels safe in his cage, so that may be why he doesn’t want to leave. I recommend keeping it cage door open, and just letting him take his time getting out. Maybe, as I said, have food out there to help, and put some hay out as well.
The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.