Why does switch change parallel current after junction?
I am confused about how pressing the switch actually changes the current being delivered to the [74HC04].


The 74HC04 has a high-impedance input. It will source or sink only miniscule currents, whether the input voltage is high or low (possibly it will sink more current at some in-between voltage, which is why we try to avoid driving it there). 

So when the switch is open, there is essentially no current through the resistor. Therefore the voltage across it is 0, and the voltage at the input to the 74HC04 is VCC.

When switch is closed, it shorts the 74HC04 to ground. Since there's now 5 V across the resistor, some current (5 mA) will flow through it and everything is consistent. Still no current flows in or out of the 74HC04 input.