In addition to the previous considerations, I will add a few more.
Stages with voltage output (such as a voltage follower) are implemented as voltage dividers consisting of two elements in series "stretched" between supply rails. One of them is "pulling up" and the other is "pulling down" the common middle point (circuit output). Thus the circuit output can both source and sink current to/from the load.
If the stage consists of only one active element, it can only source or sink current. In the considered example, the emitter follower implemented by an n-p-n transistor can only source current. This can create more problems besides those already listed.
If the load contains a positive voltage source or a "pull-up" resistor (as TTL gates that try to inject current to the previous stage) the base-emitter junction may become backward biased... the transistor cuts off... and a breakdown can even occur. The same can happen with a capacitive load (charged capacitor).
So a pull-down resistor is necessary... and it has to be low resistive enough to handle any load. But it does not work well when the input voltage varies widely because the current will also significantly vary (a typical example is an emitter follower driving the output stage of a power amplifier). In this cases, the ordinary ohmic resistor is replaced by a "dynamic pull-down resistor" (current sink).
The best solution is to change the pull-down resistance in an opposite direction to the pull-up change. This idea is implemented by replacing the pull-down resistor with another but p-n-p transistor in "complementary emitter followers" (aka "push-pull stages"). They can both source and sink significant current.