According to Fieri, you should consider that "every time you touch that burger and you hear 'chh' ... That's flavor leaving the plate." In other words, when you press your burger, you are expelling juices from the meat out onto the hot pan or grill.
Burgers, especially those cooked over high heat, should have a high surface temperature. This results in the myofibril fibers being tensely squeezed and releasing more juices and moisture from the protein. Pressing down on the burger causes a rapid release of these juices. It may sound good as they steam the outside of the patty for a (very) brief moment, but in reality, they are being cooked off and leaving your burger drier than it was before, which is why you also shouldn't flip your burger too often.