1
general::
Phrase(s): run counter to something
to be in opposition to something; to run against something. (This has nothing to do with running.) • Your proposal runs counter to what is required by the manager. • His idea runs counter to good sense.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
Be in conflict with, oppose, as in Practice often runs counter to theory. This idiom, first recorded in 1843, uses counter in the sense of "in an opposite direction."
American Heritage Idioms