Why are fatty acids synthesized in two carbon units?
The answer to this question lies in the chemistry of fatty acid synthesis — specifically the chemical energetics of the reactions. For those new to the biochemistry there is a basic concept that must be understood: that a reaction can occur spontaneously only if it involves a negative change in Gibbs Free Energy. This is discussed, among other places, in my answer to another question.
As regards long-chain fatty acid synthesis, the answer can be found in Section 22.4 of Berg et al. Biochemistry some of which I summarize here.
The reactants in fatty acid synthesis are linked to a protein during the cycle of reactions — acyl-carrier protein, ACP:
malonyl CoA + ACP ⇌ malonyl ACP + CoA
The first condensation reaction of a malonyl constituent in the elongation cycle of reactions is shown below.


The key point to note is that in this step the malonyl carboxylic acid
group is released as carbon dioxide with a substantial decrease in
free energy that makes the reaction favourable. Without it the
reaction would not proceed, which is why the synthesis of acetoacetyl
ACP from two molecules of acetyl ACP does not occur.

It is worth adding that this free energy is ultimately derived from ATP, which is needed to drive the reaction in which malonyl CoA is formed from acetyl CoA and carbon dioxide.