Why does an sp3-hybridized electrophile must have a leaving group (X) in order for the reaction to take place?

A general theme in organic chemistry is that carbon atoms usually have four bonds. These four bonds can consist of single, double or triple bonds, so long as the sum adds up to four. For #sp^3#-hybridized carbon atoms, carbon will be bound to four different atoms, each with a single bond. Therefore, in order to form a new bond with a different atom through a reaction, there will need to be at least carbon single bond that is broken.

Suppose we consider the following #S_N2# reaction:

In this reaction, hydroxide is acting as a nucleophile and attacks chloroethane, which acts as the electrophile. Notice that the #-OH^-# forms a new bond with the carbon atom, which is a favourable reaction. If there were no leaving group, however, carbon would be stuck with five atoms bound to it which is impossible. Therefore, the leaving group (X) which in this case is chloride, needs to be removed from the carbon. The image below shows the generic equation for this type of reaction, with Nu representing the nucleophile and X representing the leaving group.

It is important to note that reactions will only proceed when the incoming nucleophile is a worse leaving group (and better leaving group) than the atom already present. Otherwise, there is no driving force to cause the reaction to go.