"argued myself" is a correct and usable phrase in written English.
It means that the person has debated or discussed with themselves about a topic or situation. Example: "I argued myself into making the decision to quit my job and pursue my passion for writing."
Exact(2)
I have argued myself (in The New Yorker, back in 1995) that two states cannot be separated the way those who call for a "divorce" suppose.
I do privately accept her point that you can't beat the classic, the navy and white Adidas three-stripe, but unfortunately I've argued myself into a corner and can't back down.
Similar(58)
Yet I couldn't argue myself out of my desire.
Then, during the next national crisis, The Vietnam War and its following recession many would argue, myself included, that American Cinema hit its peak in terms of filmmaking artistry.
Why, when I set out on the road to grammatical perfection I might even have argued this myself.
There was no reason, I argued to myself, that translations of fiction couldn't be made far more extensively in and out of languages that are not a work's original.
While writing this article, I gathered my thoughts through a version of the same principle: having collated my notes onscreen, I printed said notes, scribbled all over the resulting printout, argued with myself in the margins, placed exclamation marks next to key points, spread out the scrawled result – and from this landscape hewed a (hopefully) coherent argument.
I called back, yelled, argued, resigned myself to a hopeless fate at the hands of the increasingly un-benevolent Amazon.
I've argued that myself, in the past, but the lack of any actual evidence of automation-driven net job destruction now gives me pause.
I argued with myself all the way up to the voting booth in the Massachusetts primary but at the moment of truth I went with Barack.
After all, I will talk to myself all day, and probably disagree and argue with myself as usual.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com