Why transmission gates require two MOSFETs cant one MOSFET act as a switch?
The problem is that a transistor is controlled by the Vgs voltage, and the signal you're switching determines the source voltage.  The issue is that if you only use, say, the NMOS with the gate tied to Vdd, when the signal level goes high on one side, the transistor will turn off when the output level reaches Vdd-Vt and then it will no longer be driven through the NMOS (you could pull it high with a pull-up resistor, but this will be slower than driving it high).  If you get an NMOS and you drive the gate voltage to at least Vdd+Vt, then you only need one transistor.  However, this requires a transistor that can handle that high of a gate voltage, and it requires an extra power supply rail.  So what's usually done is to connect an NMOS and PMOS in parallel and turn them both on (NMOS gate to Vdd, PMOS gate to GND) or off (NMOS gate to GND, PMOS gate to Vdd) to switch the signal.  

Another issue is that if you use one transistor, you'll get capacitive coupling between the gate drive signal and the signal being switched.  If you use two transistors, then the coupling through the NMOS gate is mostly canceled out by the opposite coupling through the PMOS gate.