Why? Because PHYSICS, that's why.
It's not about the grip of your tires. It's about centrifugal force and center of gravity. If you keep your body upright and lean the bike under you then your center of gravity is shifted to the outside of the turn and more force due to your body mass is in the *downward* direction instead of the *outward* direction. Road bike tires are designed with this in mind, have a rounded cross-section, less sidewall height, and more usable tread, to *facilitate* this.
If on the other hand you leave your ass firmly planted on the saddle, like it's glued there, you have to *slow down* more in a curve or corner than using the above technique, because your center of gravity is more towards the *inside* of the turn, and more of the force is pushing you and the bike to the *outside* of the turn, which in turn puts more stress on the ability of the tires to hold the road -- therefore you can't take the turn as *fast*.
Note that these are racing techniques. If all you're doing is riding for fun or commuting then don't even bother, just brake before the turn, go slow through it, and speed back up afterwards.
However: The OP wanted to know how to *maintain speed* through a turn, therefore we're talking about *racing* techniques for high-speed cornering on a road bicycle.