I looked it up in Merriam, it said origin, unknown. HOWEVER: cur, from the 13th-century, can mean: 'a surly or cowardly fellow'. THEN: dudgeon , from the 15th, can mean 'a fit or state of indignation'.
Why so often an older man? Need we look farther than Dickens' Scrooge?
Look up some crazy sounding 20+ character word, takes three steps, and then you get a definition of the sub-sub-sub word and it says ".... blah blah, derived from the Greek base <abc>- and then also the Latin base -<xyz>", and you realize you had no chance at getting it from any kind of first principles or anything.
For what it's worth, the first two steps in your lookup would come naturally to a native speaker- it's a suffix formation similar to e.g. "cleanliness" and "friendliness".
"Curmudgeon" itself is interesting, because while it's not particularly common, I actually think a lot of native English speakers would recognize it because it's got a lot of character- for some reason, the way it feels to say and the way it sounds almost has some of the character of the meaning.
curmudgeonliness: The state or condition of being curmudgeonly.
okay, let's look up curmudgeonly:
curmudgeonly: Characteristic of a curmudgeon; churlish
nearly there:
curmudgeon: An ill-tempered person full of stubborn ideas or opinions, often an older man.