Is this a Fallacy

“I'm sure I'll take you with pleasure!" the Queen said. "Twopence a week, and jam every other day."
Alice couldn't help laughing, as she said, "I don't want you to hire me - and I don't care for jam."
"It's very good jam," said the Queen.
"Well, I don't want any today, at any rate."
"You couldn't have it if you did want it," the Queen said.
"The rule is, jam tomorrow and jam yesterday - but never today."
"It must come sometimes to 'jam today," Alice objected.
"No it can't," said the Queen. "It's a jam every other day: today isn't any other day, you know.”

Through the Looking Glass by Lewis Carroll

Sounds like equivocation on the Queen's part.

"Every other day" is relative in a given week to a specific day. Since it's a general rule, we should be able to apply it to some sort of specific period (otherwise, it's a meaningless statement). So Alice is spot-on that eventually, 'every other day' will come to a given day - which, if the present day, would be 'today' - yet, the Queen rejects that and claims that the present day is somehow exempt from ever possibly being classified as the 'other day' previously referred to.

When done in real life, it's usually someone being facetious.

Here's another example:

"They say one should do something nice for someone. I'm someone, so you should do something nice for me!"

Here, we go from 'someone' being 'a person other than oneself' to 'a specific person' (thus equivocating terms).

Or, in the immortal words of Humpty Dumpty who said in rather a scornful tone, “When I use a word, it means just what I choose it to mean — neither more nor less.” 

One might say it is an explicit statement of the usually concealed Fallacy of Equivocation. The misleading use of a term with more than one meaning, usually accomplished by glossing over the meaning initially intended in the discussion. Restated: it is to change the definition of a word within the discussion. Often, this is a technique in concert with moving the goal posts.