It does sound odd

I don't know! I know my hands get a bit weird after cutting pumpkin cos it does something weird to my hands, so I suppose meat could do a similar thing...I would have thought it'd be a moisture thing if anything...

Okay, so a quick google search tells me that meat juice is a bad idea for dry skin - and I'm thinking - if you're washing your hands are you using soap? Like, stripping your hands of their natural protective oils and then going back to the meat?

Maybe you could just use some latex gloves when chopping meat? Or at least moisturise beforehand, maybe with an oil based moisturiser? Although...do you really want that on your meat...