Pull up resistors work because when no current is flowing through them they develop (drop) no voltage. Thus, whatever the voltage is on one side, it is the same on the other side. But when current flows a voltage develops across the resistor (E = IR). In your application, when you close the switch (push button) current flows and a voltage develops across the resistor. Thus, the voltage on the switch side must be higher than on the other side (ground). This is why you need to get rid of the resistor.

Mahmood is right also. Mechanical contacts are extremely noisy, and will cause unpredictable false switching. Look at your signal on an oscilloscope and see how many times you trigger on a single push of the button. To "debounce" your signal use a schmitt trigger inverter. This is something you have to do everytime you use a mechanical switch.