Do you need a free hand to Shove?

I don’t know if I’m crazy or what, but if you had asked me "Do you need a free hand to Shove?" I would answered with a resounding of course before I reread the PHB and noticed it said nothing of the sort. It specifically mentions you need a free hand for grappling, you need a free hand for somatic components (feats notwithstanding) and well, seems to me like adventurers cannot normally juggle more than one thing per hand. Is this an oversight for a tacit rule (therefore yes, you can only do one thing with each hand, and wielding a weapon prevents any other use), or there’s a rational reason for which you can shove a creature when you are duel-wielding daggers I’m missing, or does it make sense in-game for balancing reasons I can’t see…? Help me out here