I'm very new to electronics, but in knowing Ohms law from school (I=V/R) you know as resistance goes up, (if voltage is constant) current must decrease. And to work out the total resistance in a series circuit, you add the resistance of each component together. So when you wire them in a parallel circuit, you use reciprocals of the resistance (So the equation is 1/Total resistance=1/ResistorA + 1/ResistorB, etc). But going by this logic, a bigger resistor would equal a bigger current (Because obviously 1/2 > 1/3). Can anyone explain why this is?

1 Amp of current through a 1 Volt potential difference equates to 1 Ohm of resistance. Assuming constant voltage, if resistance decreases, current increases. Two 1 Ohm resistances in parallel is 0.5 Ohms. Two 1A currents in parallel is 2A. By Ohm's law, V=I*R, and thus 1A*1 Ohm=2A*0.5 Ohms=1V

You haven't finished the equation by mathematically inverting ("1/x") your answer. Yes, 1/2 is greater than 1/3, but when they're inverted, 3 is greater than 2. More resistance (in ohms) means less current flowing at the same voltage.