Dear Martin Kmín,
It is in my opinion «a matter for serious and important debate». It is a question about essential things.
It is a term in computer programming also.
Kindest regards,
Goldmund
My guess--in those contexts, 'high argument' = lofty, principled, high-minded, critical, of essential value, definitive, profound, deeply considered, involving superior insight--that kind of thing.
"Argument" in a poetic context can mean "the principal theme of the poem".
So you might say that Milton's "high argument" in Paradise Lost is "to justify the ways of God to men" (I.26); while Wordworth's in The Prelude is to depict "the growth of a poet's mind".
The "high arguments" of each of the books of the Old and New Testament would take a little longer to summarise.
MrP