The real answer is that CA glues were first designed to allow surgeons to glue their patients back together. For those places where stitches don't work well.

Yeah -- like in Vietnam.

In reality, though, they weren't developed for this purpose, and, in fact, OTC CAs are methyl CAs, which have issues with toxicity. Medical-grade CAs are butyl (or other longer alcohol) CAs, which don't have as much of a problem. Also, it was initially developed by Kodak to be an optically clear polymer for use in optics, but was rejected. Later, Kodak was researching it as a heat-resistant acrylic for airplane windscreens when its adhesive properties were discovered. (I have a hard time believing that the first inventor didn't glue his fingers together, but maybe the formula has been refined since. ) A little later than that, it was released as a glue product, and then a few years later, was used in MASH units in Vietnam. I don't beleve that it has ever been approved for medical use in the US, but it has almost everywhere else, and I could be wrong, too.