>Spade doesn't look like a sword!
Yes it does. Ancient swords were often made with leaf blades that the spade symbol was emulating. It could also be construed as a spearhead, but the meaning is clear; it was meant to depict the military. The suit would also sometimes be called Leaves or Pikes.
The military also included the nobility (as they were the heads of the military and responsible for leading armies on the battlefield), so the Swords suit is associated with soldiers and nobility.