Why Does My Baby Massage My Breast While Feeding?

I hope this wasn't a joke. This is a very natural thing and benefits you and baby it comforts baby in the way of touch and feel this gives much comfort and support to baby during the most needful time in their life to be nutured by you
and for you mom this serves an amazing purpose by the touch of baby's hand this is stimulating your body to release the hormone oxytocin which then stimulates milk production and secretion for feeding
this also bonds you and baby.

Because he (she) loves you.
He especially loves to touch you, skin contact is wonderful and you are his favourite person to be in contact with, after all.
Because he's a wiggly little creature.
Because the breast is there, nicely soft, and the source of all-satisfying tummy goodness (from his perspective).

Actually, that may not be true in your case, because if you're not actually breastfeeding your baby may still massage. Even bottle-fed babies like to fondle! Given the chance. Skin-to-skin contact is still craved for by little babes.

Because he loves to use his still new and exciting hands. His nervous system is all go.

If it bothers you, hold his hand with the hand on the side he's not feeding off of. Or give him a soft toy or cloth to wave around instead (he'll probably find that pretty appealing, too). I couldn't tolerate being massaged and beaten myself; it's a sensitive area, especially if the milk ducts are flowing.