The phrase 'encounter the argument' is correct and usable in written English.
You can use this phrase when you would like to refer to a situation where you become aware of an argument and must respond to it or take some action. For example, "I encountered the argument that scientific evidence proves that aliens exist, but I'm not sure I'm convinced."
Around Canberra it's possible to encounter the argument – a pretty tinny, half-hearted one – that we can't depart from our American friends on this (other US allies do, regularly – the UK, France, Germany).
As someone who is black and lesbian, it's tiring and absurd to encounter the argument that the black civil rights movement somehow exclusively owns the ability to use "civil rights".
I first encountered the argument that eventually persuaded me to change my mind about affirmative action in a Supreme Court brief filed by three University of Texas law professors in 1997.
Since it looks to ordinary speakers as if there are statues, and since they have no reason to believe that appearances are misleading (having never encountered the arguments for eliminativism), their utterances and beliefs would be reasonable even if false.
The truth is that I get a sinking feeling each time I encounter the marriage-plot argument.
The pertinacity of hard core anti-European Tories impugning any result will force the prime minister to look for allies in other parties; maybe he will be surprised encountering the unpleasant argument: If you cannot deliver your own party why should we help?
Blogging is a lot like teaching the same class year after year; you're always encountering the same arguments you've refuted in the past, and you want to demand why they weren't listening the last time.
(Yes, that sounds a touch ridiculous, but I assure you that we'll encounter that argument, loudly and immediately).
I have encountered the same diabolising argument in Denmark, Austria, Belgium and Italy: no discussion with the extreme right!
If you haven't encountered the anti-medication argument elsewhere, you are unlikely to hear it from a doctor.
We have already encountered the so-called argument of the bad lot, which, we saw, is valid as a criticism of ABD1 but powerless against various (what we called) congruous rules of abduction.
