In a non-inverting op-amp, the negative feedback input (V1) is calculated by (R2/Rf+R2)*Vout because it is a potential divider. However, why do we calculate the voltage across R2 and not for example Rf (i.e Rf/(R2+Rf))?
However, why do we calculate the voltage across R2 ...
Because the amplifier output becomes stable when \$ V- = V+ \$.
\$ A \$ is a very large number. Any difference in the input voltages, \$ V_+ - V_- \$ is multiplied by \$ A \$ and appears on the output.
The essence of the negative feedback (not just in op-amps) is to correct the output and reduce the difference between the setpoint (\$ V_+ \$ in this case) and the feedback (\$ V_- \$) as close to zero as the gain allows.
Because that's what a voltage divider does. In this case, we calculate the voltage across R2 since that's the voltage we want to know. The voltage across R2 is the voltage being applied to the opamp negative input.
For a simple explanation and derivation of negative feedback, see my answer https://electronics.stackexchange.com/a/50472/4512.
You're using a formula you memorized rather than just finding the answer with Ohm's law. The current through Rf and R2 is Vout/(Rf + R2). So the voltage at the inverting input is Vout/(Rf+R2) * R1. If you wanted to, you could also figure it as Vout - (Vout/(Rf+R2))*Rf, which simplifies to the same formula.