Why would a cynic be offended by fantasy?

There are three definitions of cynic, according to the American Heritage Dictionary:-

1. A person who believes all people are motivated by selfishness.
2. A person whose outlook is scornfully and habitually negative.
3. A member of a sect of ancient Greek philosophers who believed virtue to be the only good and self-control to be the only means of achieving virtue.

Use of the word to mean the third of these is rare nowadays; the speaker of your sentence presumably had the second definition in mind, and you looked up and found the first. The historical note includes the explanation:-

When Cynic first appeared in English in the 1500s, it referred to the Cynic philosophers, but cynic and cynical were soon applied to anyone who finds fault in others in a contemptuous or sneering way.

So in this case Judy would be offended by a fantasy as she would be offended by, or affect to be offended by, anything else (finds fault...in a sneering or contemptuous way), and the more pleasant or agreeable the fantasy, the greater the scorn of the cynic.

Well, Noah Webster's 1828 American Dictionary of the English Language actually has a very different definition of the word Cynic that's quite different from any other dictionary:

CYNIC, CYNICAL, a. [Gr., canine, a dog.] Having the qualities of a surly dog; snarling; captious; surly; currish; austere.

Cynic spasm, a kind of convulsion, in which the patient imitates the howling of dogs.

Translated into the modern tongue, they have a bitchy personality mate. People in a mean and sour mood, snappin' and snarlin' at whatever possibly just because they can. I suppose it's quite an apt and amusing way to describe the sort of people who are called cynical, although it does imply a bit more vigor than the gloomy tone we'd come to expect of the word now....

Maybe the offended cynic does not have any imagination, and views products of the imagination with suspicion. Like so many modern people, the offended cynic refuses be reminded of the missing portion of their humanity, but prefers to accuse others of ignoble motives.