Why is only one part of buffer in the reactants side?
A buffer is a solution that is meant to prevent the pH from drifting away from its intended value in both directions (i.e. the solution should neither become more acidic nor more basic than desired). For the buffer to accomplish this, two components are added one of which is intended to counteract acidic additives the other to counteract basic additives.

Whether or not these two components are conjugate Brønsted acids and bases does not matter; a solution of e.g. ammonium acetate will also buffer. Every liquid inside the human body is buffered by multiple components to a very narrow pH range, so many different compounds together can also produce a buffer effect. However, the combination of an acid and its conjugate base is typically the most effective and narrow-range buffer system available in a typical lab context — and also the easiest to set up and use.

While in the buffered solution the two components of a buffer can indeed be said to react; this can be proven with isotope labelling. For example, if you had $\ce{^13C}$-labelled acetic acid and $\ce{^12C}$-labelled acetate, these two would react in the following way:

$$\ce{CH3^12COO- + CH3^13COOH &lt;=&gt; CH3^12COOH + CH3^13COO-}\tag{1}$$

This reaction does not, however, describe the buffering action.

Buffering itself can only take place if some acidic or basic compound is added to the solution as hinted above. Depending on what is added either equation $(2)$ or equation $(3)$ will take place.

$$\begin{align}\ce{CH3COO- + H3O+ &amp;&lt;=&gt;&gt; CH3COOH + H2O}\tag{2}\\
\ce{CH3COOH + OH- &amp;&lt;=&gt;&gt; CH3COO- + H2O}\tag{3}\end{align}$$

The first equation $(2)$ is the one if something acidic is added, equation $(3)$ takes place if a basic compound is added.

As you can see, one component of the buffer basically exists to quench basic additives (the acidic part) while the other only exists to quench acidic ones (the basic part). Therefore, in a buffering equation you will only see one of the two active at once.