Superglue was one of those "accidental discoveries" like teflon, according to reports. Someone examining materials found out that it would stick things, and the applications just sort of kept popping up. It does seem to have sort of "mystic" properties, and it didn't take long to discover that it would stick people parts together.
Significant use of the basic material goes back quite a bit before the use in surgery, but early forms in which it was supplied were so incredibly expensive that only a few industrial applications were found for quite a few years.
The basic cyanoacrylate material remains liquid as long as it's exposed to oxygen in the air, so for reasonable storage life it is absolutely mandatory that the container be permeable to oxygen. It is an unfortunate fact that most materials permeable to oxygen generally are also permeable to humidity in the air, and exposure to water causes the glue to react and harden. Temperatures outside normal human comfort ranges may also cause it to set up in the can.
Handling the container with "greasy fingers" can coat the container with an oil film that shuts of the permeation of air, and can cause the glue to set up fairly quickly in storage. SOP at a lab where I worked in the late 50s - early 60s was that the worker must rinse his/her hands with pure methanol before even picking up the bottle. (The lab bought it in 1 quart jars, at about $200+/jar, '60s dollars IIRC.)
Superglue is not really an ideal adhesive for wood, or for other porous materials, since usually the hardening with porous materials occurs due to moisture, and when hardened by moisture it "clabbers" rather than setting up. This doesn't mean that it's not useful for wood, but other "wood glues" give a stronger joint than can normally be obtained with superglue.
Absolute maximum bond strength is seldom really needed. (Even into the early 1950s, wooden airplane parts were usually assembled using raw chicken blood for the adhesive. It was considered a "miracle" when someone discovered freeze/vacuum drying of the blood glue - which got rid of a lot of the smell, even though it required mixing with water before using.)
Again at the lab, workers usually kept an open petri dish with a dollop of methanol handy, beside the "crud hole" which was a vacuum port with a screen on it where you could drop bits of dirt to be sucked away. Frequent moistening of the fingers with methanol, and drying them in the vacuum-hole airflow, completely eliminated "glued fingers." Methanol will mostly dissolve and "inactivate" uncured cyanoacrylate. Propanol, common rubbing alcohol, will deactivate it, but leaves a bit of "scum" that's easily rubbed off. In an emergency, rinsing with plain water will also set up the uncured glue so that you don't get "too much into your work."
On non-porous materials, which is where superglue works best, there are simple procedures that consistently produce good bonds. Ignoring them generally gives inferior, inconsistent, and unreliable bonding. I suspect this is why British Air Ministry (and RAF?) regulations prohibit using cyanoacrylate adhesives in aircraft - they never RTFM.