While you didn't have the flush, you had the top two pair, which I am confident was the best hand. I don't think you so much outplayed him and just outflopped him.
Regarding showing hands - I don't show my cards much, but I do at times, particularly if I want some hotshot to come after me (show him one big bluff and you'll get action for hours).
In this case, had you shown your cards, you would have been showing him that he made the correct decision by folding (even though you didn't have the flush). This is positive reinforcement, makes him feel good about his play, and makes him a stronger opponent. Now, had you had complete garbage here, literally a hand like 6 high with no flush draw and you showed him THAT, then he would realize he made a mistake and it might get to him a bit and cause him to start second guessing himself.
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