The "Southern Ocean" was created in 2000....much like the arbitrary declaration that Pluto is no longer a planet.
I suppose the eggheads decided that since the temperatures of the water around Antarctica were different from the other oceans, the latitude where the temperature shifts (60 degrees S) is the arbitrary boundary of the Southern Ocean.
Neither decision was arbitrary and in both cases much of the scientific community had made that switch before it became "official." Sailors and scientists alike have mentioned a "Southern" or "Antarctic" Ocean for decades but since it was difficult to define it's limits it did not become "official" until fairly recently. The Southern Ocean has much to distinguish itself from the Pacific, Atlantic, and Indian so separating it made sense.
As for Pluto, I won't go in to detail since I don't want to drag this thread off topic but if you're unhappy about its demotion I'd ask if you feel similarly about Ceres, another former planet that was demoted for the exact same reasons Pluto was: it was discovered to be one of a multitude of similar objects in the same general vicinity.
Returning to the Southern Ocean, or Antarctic Ocean if you prefer as both terms are acceptable, geography often has to deal with very fuzzy concepts of borders and naming and it is very common for different groups to go about things differently. Not only does the number of oceans fluctuate but so do the continents. In the US we are generally taught that there are seven: North America, South America, Europe, Asia, Africa, Australia, and Antarctica. In other parts of the world the Americas are combined, or Europe and Asia are combined, or both of these. Borders and numbers are fuzzy things because they are human definitions and different humans often have different options.
Is Egypt part of North Africa or the Middle East?
Is Mexico part of Central America or not?
Is Greenland part of North America or Europe?
Is New Guinea part of Asia or Oceania?
You can do the same thing with bodies of water - does the English Channel extend far enough west to include the island of Ushant or is this island actually in the Celtic Sea? The island itself doesn't move around, just where you draw the boundary.
Geography isn't the only field where technical definitions can be hard to nail down, or where these definitions don't necessarily line up with colloquial understandings. If you go by botanical definitions a tomato is a fruit, a cashew is a drupe, and peanut is a legume. Does this mean it's wrong to define them as a vegetable, nut, and nut respectively? I'd say no. In terms of scientific definitions yes it is incorrect to call a tomato a vegetable but colloquially this is how it's understood and I don't see anything wrong with picking up a package of "mixed nuts" rather than a package of "mixed nuts, drupes, legumes, and seeds."
What about dates? Since our calendar starts with year 1 the first decade was the years 1-10, the second was 11-20, the third was 21-30 . . . which means that the 1970s technically encompasses the years 1971 through 1980. However when someone colloquially uses the term "The 70s" they generally mean 1970 through 1979.
If an individual feels there are four oceans that is their decision to make. If geographers and scientists want to deal with things at a more technical level they need to have more explicit definitions. Sometimes, like with tomatoes, this can clash with normal usage. Sometimes, as with almonds and Brazil nuts this goes beyond normal usage - the colloquial term "nut" often encompassing several more technical classifications. However you should really explore why these technical definitions are made before calling them "arbitrary." The Southern Ocean has currents, weather, topography, and ecosystems that tie it together and separate it from the Atlantic, Pacific, and Indian ocean. As scientists learned more about the waters around Antarctica it made sense to define it as a separate body of water - although as I mentioned at the very beginning plenty of people started doing this years ago even if the general populace of many countries went in a different direction.