In short, it's because fatty acids are made from two-carbon blocks.
The way that most organisms make fatty acids is by the successive addition of two-carbon units (acetyl-CoA). So we usually get even-numbered fatty acids just because the building blocks are also even.
In plants and in synthetic contexts, we can have some reactions that can produce odd-numbered fatty acids (by building with two-carbon units three times to get six, and then breaking that six in half to get three, for example). Such odd fatty acids are seen in some organisms, but humans are usually thought to get them from other sources (e.g. microbiota, diet).
Point 1: Fatty acids are generally built two-carbons at a time.
The European Bioinformatics Institute has a really good explanation of fatty acid synthesis. The quote below is from that (https://www.ebi.ac.uk/interpro/potm/2007_6/Page2.htm):
"Whether existing as one complex or as independent enzymes, the
reactions catalysed by types I and II fatty acid synthases are the
same. Both systems are primed with acetyl-CoA, and then add 2-carbon
units to the growing chain using malonyl-CoA as substrate."
Point 2: Odd-numbered fatty acids can be produced by various organisms, and can be linked to dysfunction in humans.
doi:10.1038/srep44845 talks about the importance of odd chain fatty acids in disease as a preface to its findings about the sources of such fatty acids. They try to narrow down where odd-chain fatty acids come from, but they definitely seem to be building their case on the pretense that odd chain fatty acids are not great in humans.
"According to the literature, the origin of C15:0 and C17:0 has long
been attributed to the diet, specifically from ruminant fat as the
main contributor in a typical Western diet. This has been explained by
the fact that these two OC-FAs are produced by the rumen microbiome
and then incorporated into the fat deposits of the host animal
destined for human consumption."
Point 3: Plants produce odd-chain fatty acids
An established/old paper (doi:10.1006/abbi.1994.1110) mentions this, and there's a Wikipedia article (https://en.wikipedia.org/wiki/Odd-chain_fatty_acid) that paraphrases in a nice way:
Some plant-based fatty acids, however, have an odd number of carbon
atoms, and Phytanic fatty acid absorbed from plant chlorophyll has
multiple methyl branch points. As a result, it breaks down into three
odd numbered 3C Propionyl segments as well as three even numbered 2C
Acetyl segments and one even numbered 4C Isobutynoyl segment.