"Pressing hard enough" -- this is a bit tricky for beginners. (Ask me how I know ... !) The instinct is that if the cheese is too wet, I must need to press it more (with a higher weight). But pressing with too much weight too soon can close up the rind before all the whey has had a chance to trickle out, trapping it inside the cheese. In general, you want to press with just enough weight to keep a gentle trickle of whey flowing, and end up with only as much weight as needed to get a smoothly closed rind within the time frame needed. (Note that cheeses that are brined/salted after pressing generally need to be finished pressing by the time the pH reaches 5.3 or so - which may only take a couple of hours, or may take overnight, depending on the milk and culture(s) used, temperature, etc.)
So if pressing more is not the way to reduce moisture, what is? Several factors contribute: flocculation - how much rennet and how long the curd has been allowed to coagulate; cut size - cutting smaller results in drier curds; amount of stirring - more stirring reduces the moisture left in the curds; amount of cooking - cooking to higher temps and/or for longer will reduce the moisture left in the curds.
Part of what makes cheesemaking an art is juggling all of these variables, and more -- so that you reach the right pH at the right time with the right level of moisture in the curds. But that said, there is room for a good bit of variation that still leads to good cheese - maybe not quite the cheese type you intended to make, but still good.