I had exactly the same issue just the other day. I was given a near brand new Golf as a loan car, and wanted to position the visor as you describe. I had to pull with such force that the retaining clip came out of the roof lining. Even then I needed to use the vehicle key bit to release the clip off the visor. Thankfully all went back together easily but I decided to leave it well alone.
I think they are just held very tight, especially if used infrequently. You could try unclipping/reclipping the visor a few times, or slightly widen the jaws of the clip with the barrel of a suitably sized screw driver, or possibly just a touch of lubricant spray will sort it.
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