After finishing dinner, Sidney Morgenbesser decides to order dessert. The waitress tells him he has two choices: apple pie and blueberry pie. Sidney orders the apple pie. After a few minutes the waitress returns and says that they also have cherry pie at which point Morgenbesser says "In that case I'll have the blueberry pie."
The most trivial example is that he simply changed his mind—but obviously this has nothing to do with IIA.
Another reason is that he might be dining with someone (who is, perhaps, away from the table). Say that he knows his partner's preferences are C>B>A. Say his own preferences are B>A>C, but that he also has a preference for being able to sample two distinct choices. Initially, he believes that his partner will order B, so he orders A to maximize his range of desserts. Upon learning that the "irrelevant" choice C is available, he will have to order his top choice, B, himself.
The same scenario could play out with himself as the second diner, in the sense that he knows he will have two opportunities to visit this restaurant (and that their dessert choices will remain constant). If his preferences are C>B>A, and for whatever reason he decides to order his second-most-preferred dessert first and his most-preferred dessert on the next visit, then his choice is logical.
Perhaps he's of the opinion that a kitchen which prepares cherry pie cannot prepare an adequate apple pie.
The point is, alternatives are rarely "irrelevant". In fact, including the word "irrelevant" in IIA is begging the question: we are tasked with determining whether dominated alternatives (for example) really are irrelevant, and our answer might be "no".
For the second case, you've made "good apple pie" and "bad apple pie" different elements of the choice set. And again, IIA implies that if "good apple pie" ≿ "cherry pie" that continues to hold when "bad apple pie" is an option. (And as an important aside, all cherry pie is of equal quality in this hypothetical.) Also note that it has nothing to do with the relative likelihood of different choices being delivered, so choosing to order something because you think another order is likely to be messed up is perfectly consistent with the IIA.
Arrow's impossibility theorem is a mathematical result, and IIA is a property of a mathematical representation of preferences. They have practical implications, but certainly don't imply that people in real life make transparently consistent choices.
Delving further down this tangent... If that's what happened, he would be unlikely to have said "In that case, ...". That usually means "I am incorporating this new information, and it has changed my decision." More likely he would have said, "On second thought..." or "Actually..." or "Y'know..."
Not, of course, that this has much relevance outside of considering English pragmatics.
Say there's an election between a moderate democrat "blueberry pie" and a third party liberal "apple pie". As a liberal, Sidney would rather vote for the third party ("Sidney orders the apple pie"). However, if you introduce a republican candidate "cherry pie", Sidney will probably vote for the democrat (blueberry pie) instead of the third party candidate, because he'd be worried about his vote costing the more moderate candidate the election.
IIA means that you won't vote differently than your preferences—but people do that all the time. And sure, a voting system where that wasn't necessary would be nice, but losing that condition isn't as nonsensical as it seems at first.
(with the caveat that it has been a long time since I've thought about these results.)
Ask your dinner party "Do we prefer Apple or Blueberry?", and a majority might reasonably answer Apple. Ask them "Blueberry or Cherry?", and a slightly different majority might reasonably answer Blueberry. Ask them "Cherry or Apple?" and a different majority would answer Cherry. You would get this situation, for instance, with the following voters: 2x A > B > C 2x B > C > A 1x C > A > B A beats B by 3:2, B beats C by 4:1, and C beats A by 3:2.
This is a rock paper scissors situation -- or a "condorcet cycle".
Now suppose instead of simple Sidney there were actually these 5 people ordering dessert. Is it really that unreasonable that the group as a whole might pick blueberry once cherry is on the table even though a majority prefers apple to blueberry?
What is IIA? Can't find anything relevant on Google.
(Except that it might -- e.g., imagine that making cherry pie is incredibly difficult and most kitchens can't manage it, and that the special skills and equipment required are also useful for making really good blueberry pies. Then knowing that cherry pie is on offer could actually be evidence that the blueberry pie will be good. This is maybe just a tiny bit similar to, e.g., changing your vote from A to B when you learn that C is standing, because C is a terrible candidate but might win, and in scenarios where C is close to winning B is C's main rival.)
That's just strategic voting, not an actual change in your preferences. How you go about voting strategically depends on the voting system in use. In your hypothetical scenario you make the unstated assumption that the voting system in use would not allow for you to express a preference for A over B without hurting B's ability to beat C. The inability of that voting system to fully capture your preferences is forcing you to vote misleadingly based on your knowledge of how others will probably vote.