My take is this:
Equality means that if a couple were to split up, each would still be able to maintain a respectable standard of living (without alimony, which doesn't count lol), but as a team, they bring each of their capabilities into a pretty nice existence that is at least the sum of its parts.
Equality means having your own assets and education independent of your partner.
It means splitting up responsibilities based upon what each person likes to do, and is good at, instead of 'because you are a man' or 'beacuse you are a woman'.

I hate washing dishes. I love cooking. My equal partner hopefully would be someone who thinks that loading the dishwasher is a good trade for a gourmet meal! I don't mind cleaning the bathtub, but can someone taller than me PLEASE deal with the shower curtain hangers so I don't break my damn neck?
See what I'm getting at?

Equality means a division of labor that does not cause resentment in either party.