it's all really an effect of high amplification. An op-amp with no feedback seems to have only two output states, "high" [voltage to or nearly to the positive-rail] and "low" [voltage to or nearly to the negative-rail], BUT, what is really happening is there is a very small voltage span where the op-amp functions in an "active region" where the voltage is somewhere between high and low, as determined by the equation Vout = A*Vin where 'A' is the open-loop amplification.
If A, for a particular op-amp is, say, 100,000, and the op-amp [lets say it's a ideal op-amp so it's output can go from positive-rail to negative-rail (or "rail to rail")] and it is supplied by a ±10 volt supply (thus the output can swing from +10 to -10 volts), then if the non-inverting input is 50µV higher than the inverting input, there will be 50µV*100,000 = 5V on the output. Any voltage at or higher than 100µV will raise the output to 10V. If the voltage on the inverting input is 100µV or more higher than that on the non-inverting input, the output will swing to -10V. This will be the case no matter what kind of feedback you add to the op-amp.
This is the key to understanding all the other op-amp circuits.
It's because the active region is so small that it becomes negligible in most op-amp configurations, in a negative feedback arrangement, where the overall gain of the amp is reduced in order to achieve stability, the feedback drives the op-amp towards this narrow active region. If this region is reached, then linearity is achieved. Otherwise the output will be at one rail or the other, because the conditions were such that the active region couldn't be reached. There is no 'magic' or 'intention' involved [i.e. the op-amp isn't capable of "wanting to make Vn = Vp"]. It is merely the op-amp following the principle outlined in the first two paragraphs.
