How paradoxical this seems is up to the reader's preferences. In any case, it makes reasoning about human actions and values more complicated than it would be if preference were a transitive relation, for then it could be treated in analogy with the mathematical notions of "smaller than" and "equal".

As it is in fact, it makes it difficult or impossible to compare the judgments of value people make as if they are made in one single scale of judgments where items are linearly ordered as if they are numbers.

Part of the explanation for the paradox is that people often use different standards for preferences, and may do so without being conscious of it. Thus, one may prefer Anna over Bertha, since Anna is sexier, and prefer Bertha over Cherry, since Bertha is more intelligent, but prefer Cherry over Anna when considering both intelligence and sexyness - or more generally, find when comparing A and B one does so in terms of standards S₁; when comparing B and C one does so in terms of standards S₂; and when comparing A and C one does so in terms of standards S₃.

Of course, when one's preferences involve several standards or metrics at the same time - as seems to be the case when judging most things - things get still more complicated.

The paradox of preference makes it difficult to work out adequate mathematical theories of utility or value, that conform to how people really make these kinds of judgments. 

Incidentally, Richard Jeffrey, in "The Logic of Decisions 2nd Edition" works around it by simply insisting that the preferences he uses in his system are and must be transitive. This makes sense in so far as one needs and wants and has preferences that are comparable in some simple scale, but then it still seems examples like given above (in brief: different standards for comparing different pairs, rather intuitively from the properties of the items in the pairs) are quite normal, quite human, and not transitive for obvious reasons.

Another thing it makes most doubtful are human scales of judgment in which all things are measured and ordered from most excellent to worst possible, and everything gets a rank and degree in the scale. Such scales are quite common, acceptable and indeed mandatory in all manner of totalitarian contexts, but they cannot hold true for humans whose preferences are not always transitive.