Why can't you know position and momentum at the same time?

You can't know both because position and momentum are two questions with no joint answer. Socks then shoes is a different operation from shoes then socks, and asking position then momentum likewise differs from asking momentum then position. The difference between the two orders, called the commutator, is a fixed amount with Planck's constant in it. No apparatus appears in that statement, so no better apparatus shrinks it. The uncertainty relation reads that amount as a floor under the spread in position times the spread in momentum. Squeeze an electron into an atom-sized region, a tenth of a nanometer across, and the spread in its speed cannot drop below about six hundred kilometers a second. There is no state of the electron with a sharp position and a sharp speed, so the measurement has nothing to disturb.