‘agonise’ or ‘agonize’, both are acceptable
I feel sorry for Prince Charles. He sends a perfectly sympathetic and decent letter to the President of France, Emmanuel Macron, sympathizing with him over the fire at Notre Dame, and another fire storm breaks out. A fire storm of conspiracy theories. Simply because he has spelt the word agonizing with a z. Social media users see the hand of Meghan, Duchess of Sussex, because -ize is thought to be an Americanism. Really? Come on.
Oxford dictionaries show ‘agonize’ as standard British spelling
Oxford probably prefer this spelling because the -ize spelling is older than the -ise spelling. You could say it’s more traditional. In a recent article The Telegraph quotes the Oxford English Dictionary, saying that agonize could come from late 16th century French, or the late Latin agonizare from the Greek agonizesthai. So the z spelling goes back a long, long way. Nothing to do with Meghan.
Yet most Brits think -ise is correct
Personally, I prefer the -ize spellings – except for certain words that even Americans spell –ise, for example, advertise. This is probably because of the word advertisement usually being spelt with an s.
The predictive text on my phone or computer puts a wiggly red line whenever I use an -ize instead of an -ise spelling. So the linguists working for software giants like Microsoft and Apple think -ise is the correct UK English spelling. Or perhaps they just think I don’t know how to spell!