Because more people or larger objects use the double door. In both cases, it has nothing to do with you as user using the door, so you're wasting brain cycles thinking about it. It's a door. Walk through it.
it takes effort on our part to realize that size differences does not imply functionality difference.
No it doesn't. Size may imply significance difference (which is the "why" you're looking for) but I can't think of many cases where it implies functionality difference. A double door serves the same purpose as a single one.