The phrase "contrary arguments" refers to different viewpoints or reasons that go against each other. It means there are different opinions or evidence that oppose or conflict with one another. Full definition
Inevitably, detailed attempts at contrary argument by the climate science rejection movement closely mimic the kind and quality of pseudoscience practiced by evolution rejectionists. (realclimate.org)
«The Government, when presented with the opportunity to make contrary arguments, made no argument and offered no facts. (newsday.com)