Unless by some chance there is a woman who plays or coaches in the NFL successfully (not just 'the first' or 'the only') or maybe gains recognition in her own right as a sportswriter, I don't think she should be calling a game. One of the nicer things about the 21st century is most people believe that if you've earned it, you've earned it - regardless of race, gender, etc. Otherwise what merit does anyone have to call a game above the rest of us at home on the couch? Picking a woman to call a game for the sake of diversity or political correctness rather than her own merit (as a man would) does no one any good in the long or short run.
By this argument, I don't think men announcing gymnastics or figure skating or whatever are that creepy because men have also earned merit in those sports. However, if somewhere in Bizarro world childbirth was an Olympic sport, I would be kind of unsettled if a man was doing the play-by-play.