Karen is subtly insulting you as a cope for you beating her. She's implying that the only reason she lost is because she's using her favorites and that you, by beating her, are using "strong" Pokemon and therefore your victory means less. It is a true scrub mentality, though it could be she's just pissy at you because she's a Dark type trainer and just can't let a defeat go.
The Gentleman is speaking from experience and is trying to guide players that want to compete at the highest level. As you face stronger and stronger opponents, you need to place yourself on equal footing by using the strongest tools available to you. Using a broomstick to play baseball in your backyard is fine, using it when stared down by a major league pitcher is just asking for failure.
