Apparently sometimes $1/2 < 1/4$?

Simply put this is a travesty. The question asks, what appears to be a simple question about two real numbers, $\frac{1}{2},\frac{1}{4} \in \mathbb{R}.$ In particular, it appears to ask if $\frac{1}{2}>\frac{1}{4}.$ The answer to this question is clearly, under normal construction and ordering of the reals, a resounding YES.

What the question meant to ask is a question about fractions of potentially different quantities. In particular, from the teachers drawing, the question meant to ask if $$\frac{1}{2}\cdot x>\frac{1}{4}\cdot y, \qquad \forall x,y \in \mathbb{R}.$$ The answer to this is again, very obviously no, but this is not what the question asked...

Awful, awful, awful question. The intended wording ought to have been along these lines:

Is $1/2$ of something always greater than $1/4$ of another thing?

Your son reasonably interpreted the question as referring to the ordering of real numbers $1/2$ and $1/4$, as David mentioned.

What to do now? Well, certainly bring it to the educator's attention. They may be unaware of the flaw, or they may have seen it and decided to fudge it (not cool in that case!). But more importantly, there is a lesson to salvage from the wreckage. This a learning moment. There was a major failure in the question. Ask your son why he thinks he is correct, if he sees the intended purpose, how would he would correct the wording, how he thinks the mistake could have been avoided, and what he feels about the whole debacle as it stands.

It's a good point to recognize that mathematics is not only a toolkit to handle computation and understand nature, but a form of communication. Language is essential.

What is missing in the question is the notion of units, or dimensions: greater in what? An inequality like $\frac{1}{4}<\frac{1}{2}$ should assume an equivalent unit on both sides. Speaking of the volume of a liquid, one "could" say:

$$\frac{1}{4} \textrm{(of a liter)}<\frac{1}{2} \textrm{in dm}^3$$

because one liter is one cubic decimeter. But saying

$$\frac{1}{4} >\frac{1}{2} $$

when the LHS is in kilometers and the RHS in micrometers, without mentioning it, is a twist to inequalities: they "should be" unit-independent. Or at least equipped with an order relation that axiomatizes the expectations. You could as well define "greater" as the largest on the denominator of reduced fractions. But this would be a very mundane "greater" definition.

What this can teach you is to be aware of logical fallacies in the real world, like a merchant offering you a price so good that he loses money on it. This could incite you in a duel in the manner of the barometer question:

A physics student at the University of Copenhagen was once faced with the following challenge: "Describe how to determine the height of a skyscraper using a barometer."

The student replied: "Tie a long piece of string to the barometer, lower it from the roof of the skyscraper to the ground. The length of the string plus the length of the barometer will equal the height of the building."

an anecdote mocking the stereotypical answers sometimes required from students.