Some definitions I have seen are: "catarolysis - n. - cursing to let off steam" and "catarolysis: letting off steam by cursing" and "catarolysis /kat uh RALL ih sis/ n The practice of cursing to let off steam"
So far I see that "lysis" means "to break down"; and "cata" means "downward movement"; but that doesn't seem to fully cover "cataro"...
Even if this is just coining for fun, how might the root words better match the definition?
It's not an actual word, which means there's no established etymology. That said, what you're probably seeing is some 19th century latinate slang—they just loved talking uppity latinate nonsense—that someone put into a dictionary as a lark and has since been unthinkingly copied by subsequent volumes. In any case, you can see at Google Books that the only real 'use' it has is in collections of odd old words.
It's presumably based on the Greek κατάρα ("a curse", "cursing"¹) that shows up a few times in the Bible, plus the medical suffix -lysis from Greek λύσις ("a loosening", "an emptying"). There's no actual connection with steam, whose constant inclusion seems to underline that the word lists including it are just copying one another.
¹Strong more specifically glosses it as "what has 'to go down' due to condemnation, i.e. the penalty-curse that results when God Himself curses... something."
My guess is that the root of the word is from cathar, a member of catharism, a heretic medieval movement, from which, probably, the notion of “cursing”.
It looks to me like a portmanteau of catalytic and electrolysis. Electrolysis often uses a catalyst and emits gases.
