"I agonized over which shoes to wear with this outfit."
This usage of agonize comes closest to its Greek roots.
Back in the day, "agon" meant "struggle" or "contest." Although "agon" could refer to the kind of contest you have in an athletic competition, my favourite use of the term occured in the theatre.
|Greek Comic Masks (Source)|
Of the agon, Wikipedia notes: "The character who speaks second always wins the agon, since the last word is always hers or his."
I don't remember all of my Greek drama readings well enough to know if this claim is true or not, but it's interesting. It means that in both comedy and tragedy, the antagonist always wins the agon. In tragedy, this makes sense. In comedy, it makes a kind of sense too. Greek comedy often valorizes the person who doesn't follow the rules, but who rises to the top anyway. Although this person is usually an opposing force to the powers that be, and technically an antagonist, he stirs up the status quo and makes life worth living again.
So the next time you have an argument, feel free to claim that you're agonizing. And make sure you get the last word.