Can I use the word 'antithesize' in my essay, even though it's not technically a word?

Slightly difficult issue. Though unusual, the verb "antithesize" is most certainly a word ...

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antithesize, v. (rare)

To form antitheses; to put into antithesis.

1790 R. Burns Let. 13 Feb. (1985) 392, I can antithesize Sentiment ...

- Oxford English Dictionary

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... and one that has been used in perfectly respectable modern works of literary criticism. See Google Books https://www.google.com/search?q=%22antithesize%22&... ... for example, you don't get much more respectable than Harold Bloom and Robert D Fulk:

"The task of Book 3 is to antithesize the first two books" - John Keats, Updated Edition, Harold Bloom, 2009

" The envy of the evil hall-retainer and the avarice of the evil gold-king antithesize the Germanic comitatus ideal ..." - Interpretations of Beowulf: A Critical Anthology, Robert D Fulk, 1991

The question is, will whoever marks your essay know this? I read a lot in this territory, but still had to look it up (out of reflex, because "X is not a word" statements are so often wrong) and was surprised to find it real.

You might be safer to write something like "The artist has cleverly reversed the traditional passive female stereotype ...".

Yes, you can put it in quotes and also perhaps re-write it to make it all a little less complicated. Try this:

The artist has cleverly "antithesized" the traditional passive female. Not only is the male now passive, but the viewer also is forced to acknowledge the active female.

(We know it's a 'rendering' of some kind since it's an artist that's doing it, so I think you can eliminate that word.)

Since you are modifying an existing word in order to convey your meaning, it is proper to put that word in quotation marks to alert the reader.