Rinus Michels, a great Dutch coach, said there's only two general systems in soccer: playmaking and counter-attacking (active or reactive). The pressing belongs in the active system. Counter attacking "lets" the opponent into your half, so your team can have room to counter into.
Further, who are the worst ball handlers on your team? Probably the defenders, so pressuring defenders makes more sense than midfielders becuase there's a greater chance they'll cough it up. Since the 90s there's been the no pass back rule, so after the ball is in play the goalkeeper cannot pick it up again (wasn't always the case). So when the other team is on a "full court press" they need to be able to pass back to the gk as a safety valve. But it's also momentary as soon as they pass back to the keeper the opponents will chase it down hoping the gk will cough it up.
Most youth teams will not pass back to the keeper but that's mainly because they stick guys who can't play with their feet in goal.
One of the most basic rules about passing back to the keeper is to not make a pass that IF THE KEEPER MISSES THE BALL it will not roll into your own net. ALWAYS make the pass wide of the goal.
Hope all this makes sense.