It’s a total non sequitor, which we know thanks to this article: Kimble, James J., and Lester C. Olson. “Visual Rhetoric Representing Rosie the Riveter: Myth and Misconception in J. Howard Miller’s “We Can Do It!” Poster.” Rhetoric & Public Affairs 9.4 (2006): 533-69. Kimble and Olson conclude that the feminist message of this poster was limited in WWII; it was basically produced for internal use at Westinghouse alongside many more posters that depicted women in traditionally feminine wartime roles. 

On second thought, the comparison may be more apt than I thought.In World War II, women were encouraged to apply their domestic skills to the technical workplace with such jinglas as this one from the Women’s Bureau bulletin, “What Job Is Mine on the Victory Line”?

If you’ve sewed on buttons, or made buttonholes, on a machine

You can learn to do spot welding on airplane parts.

If you’ve used an electric mixer in your kitchen,

You can learn to run a drill press.

If you’ve followed recipes exactly in making cake,

You can learn to load shells.

Maybe this poster is implying something similar: 

If you’ve been a beauty pageant winner,

You can learn to give speeches in front of millions.

If you’ve slaughtered and dressed a moose,

You can learn to lead our country in battle.

If you’ve been mayor of a small town,

You can learn to be vice president of the nation.