It's common to hear words protagonist and antagonist. And based on the way they sound, and their opposit meaning, I always thought that they should have the same etymon, with pro and an being prefixes that change their meanings in regards to one common meaning of tagon for example.
Then one day I checked them out, and to my huge surprise, they are completely irrelevant.
Coming from the world of mathematics, I can't simply accept the probability of these words having different origins, yet having a lot of similarities in spelling, meaning, and usage contexts, annd also being opposite of each other.
My question is, how can we make sure that our etymological analysis is correct? Because after all we've seen that we were wrong in many scientific fields.