Are spellings like privatize and organize Americanisms?

No, not really. British spelling has always recognized the existence of variant spellings using the suffix
-ize/-ise. When American spelling was standardized during the 19th century (mainly through the efforts of the great American lexicographer Noah Webster), the consistent use of -ize was one of the conventions that became established. However, since then the -ise spellings have become more popular in Britain (and in other English-speaking countries such as Australia), perhaps partly as a reaction against the American custom. Spellings such as organisation would have struck many older British writers as rather French-looking. The Oxford English Dictionary favoured -ize partly on the linguistic basis that the suffix derives from the Greek suffix -izo and this was also the style of Encyclopaedia Britannica (even before it was American-owned) and formerly of the Times newspaper.

The main advantage of the modern
-ise habit : Lazy spellers do not have to remember that there are several important words which cannot properly be spelt with -ize. These include words which are not formed by the addition of the -ize prefix to a stem, but by some other root which happens to end in the same syllable, such as -vise (as in televise), -cise (as in incise) and -prise (as in comprise).

The American system resulted in the creeping of
z into some other words where it did not originally belong. Writers of American English should be aware of some spellings that are regarded as incorrect in the UK, notably analyze.

Differences Between British Spelling & American Spelling : List - 1

Differences Between British Spelling & American Spelling : List - 2

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