Well, I've given it some thought, because it did bother me when I first saw the movie, but let's think this through...
This is Superman fighting Batman (even though Superman knows Batman is Bruce Wayne, Batman does not yet know Superman is Clark Kent, IIRC). Batman/Bruce Wayne has made it abundantly clear to both Clark Kent at Luthor's party and to Superman during the fight, that he sees Superman as an inhuman alien.
So why should Superman say "save my mom"? He's close to passing out/dying, so it makes sense that he says "save Martha..." maybe he couldn't finish with the "Kent", who knows?
But it's not far-fetched to think that he would appeal to Batman's sense of duty towards saving innocents, so he asks Batman to go save a helpless civilian, he's bascially saying "by fighting me, you're letting them kill an innocent person, go save her!"