The figure to the right shows two capacitor symbols connected in series. As a starting point, let's assume that these are two identical capacitors. The connection between them is assumed to have no resistance, and therefore no effect on the behavior of these to capacitors or any circuit in which they may be connected. Therefore, this connection may be any length, covering any distance, without having any noticeable effect.
Series capacitors with no separation between them.
This being the case, let's shorten the distance between capacitors to zero. This means that the connected plates of the two capacitors will actually touch, as shown in the second image to the right.
Next, we recognize that the thickness of that center plate is unimportant; it's simply a broad conductor between the two capacitors. Therefore we can make this center plate as thin as we want. Therefore, at least in theory, we can reduce it to atomic thickness without any effect on the capacitance of the series combination.
Series capacitors with the center plate removed.
But that center plate is nothing more than an equipotential plane in the middle of an electric field. Since the outer plates are still parallel to each other, removing the center plate won't change the total electric field. This leaves us with a single capacitor, but with the plates spaced twice as far apart as for either of the original capacitors. As a result of this, the combined capacitance of the two identical capacitors in series is just half the capacitance of either one.