I have a similarly bizarre little story that's sort of the opposite: I recently added a leg to a trip and cut my fare.
Just before the holidays, I was trying to get a flight from LAX to SLC. I tend to fly Southwest, but was finding the fares higher than usual -- generally I can get something in the $250-$300 range, I was seeing $350ish.
I was offered a ride to Sacramento, so I checked SAC -> SLC and found I could purchase that flight for $200. I booked it.
There are no direct flights from SAC -> SLC on Southwest, though. Mine, as it turned out, stopped over in... LAX.
This is actually not "bizarre". It's not even unusual. And it has a perfectly rational explanation.
Suppose there are three cities: City A, City B and City C. And for simplicity's sake, suppose that City B is the hub for the airline.
Let's say B and C are major business destinations with a lot of business traffic between them. Business travelers are less price-sensitive since they're not personally paying the fare (they just have to stay within corporate travel rules), and more concerned with things like flight length and schedule.
But City A, on the other hand, isn't really a major business destination. People who want to go from City A to other cities are likely on personal/tourist travel, and those passengers do one and only one thing: punch the origin and destination cities into a travel-search engine, and pick the cheapest ticket. All other considerations are null.
Now, suppose that you are the airline employee in charge of maximizing revenue. Getting money out of the B -> C route is easy -- you just need to know a bit about corporate travel policies. If most companies auto-approve any ticket under $500, for example, you could set the fare at $499 and, so long as the flight is short and at a good time of day, you'll get business travelers paying it.
But what about pricing for trips out of City A? They need to connect at your hub in City B, but again you have to remember that price is the only consideration that matters to those passengers. So you set the fares out of City A as low as you can manage while still being profitable (and it may even turn out that B -> C has to subsidize the routes out of A a bit).
The result is, often, that A -> B -> C is cheaper than B -> C.
Similarly, for some city pairs, A -> B -> C will be cheaper than A -> B, which creates an incentive to buy the A -> B -> C ticket, not check a bag, and then just walk out of the airport in City B. This is "hidden city" ticketing (because it's "hiding" the fact that your real destination is the connection point), and airlines will usually penalize (through revocation of frequent-flyer accounts, etc.) passengers who do this.
Just before the holidays, I was trying to get a flight from LAX to SLC. I tend to fly Southwest, but was finding the fares higher than usual -- generally I can get something in the $250-$300 range, I was seeing $350ish.
I was offered a ride to Sacramento, so I checked SAC -> SLC and found I could purchase that flight for $200. I booked it.
There are no direct flights from SAC -> SLC on Southwest, though. Mine, as it turned out, stopped over in... LAX.