All of the typewriters I used in my life up to the Selectric had ribbons that had a strip of black and a strip of red. You could buy all-black ribbons, but the red and black ones were more readily (heh) available, and what I want to know is–why? I never saw anything typed in red. Once in about 11th grade I did my history homework in black (for the questions) and red (for the answers). I thought that was great–it looked like the new testament gospel–but my teacher was not pleased. What was the point of all this?
Back in the day before computers, typewriters were used for more than just writing letters. For example, bookkeeping ledgers were done on typewriters, and red was used to indicate negative balances in an account (hence the term “red ink” – although this usage pre-dated typewriters).
We’ve all had teachers without any imagination. She obviously was one of those. You forgot the rule to “know your enemy”. 
Accounting. Hence, I assume, “In the black”/“In the red.”
I’m not sure how expensive ribbons were, but maybe it was just designed to sell more ribbons. A black-and-red ribbon would last about half as long as an all-black ribbon. You’d have to replace the whole ribbon when you ran out of black ink. (Though I remember, playing with a typewriter in the late 80s, typing in red once the black ink ran out. The ribbon was probably irreplacable by then.) Maybe there were some people who did need to type in red – but I wouldn’t think there’d be enough to warrant most ribbons being two-color. Black ribbons might have been harder to find because they lasted longer, and were more profitable. It’s for a similar reason that color ink cartridges for printers have cyan, magenta and yellow ink in the same package: run out of yellow, and you have to buy another $30 cartridge.
I believe the red ink could also be used when marking edits to a manuscript.
The accounting use was the most common one, though people could use the red ink for any purpose they wanted.
They sold all-black ribbons, too. If you didn’t need the red, that’s what you’d pick up.
Typewriter ribbons were also used on accounting machines. A bookkeeper would have a leger page for each customer. The page would go into the bookkeeping machine (looked like a weird typewriter), the beginning balance entered, debits and credits (credits in red) were entered and printed, and a new balance printed.
I used to be able to get black/blue and red/blue ribbons for my Brother portable years ago in Sweden.