A nonsensical argument is when someone says things that don't make sense or have logical reasons. It is confusing and lacks proper evidence or reasoning. Full definition
And it's appealing because the U.S. system leads to all sorts of nonsensical arguments about whether golf buddies or prostitutes have duties of confidentiality, and who needs to know who got paid for breaching those duties. (bloomberg.com)
There have been so many nonsensical arguments made about Europe by both the Leave and Remain camps that it's sometimes exhausting just to keep track, but the ones being made by the prime minister are worthy of special attention. (politics.co.uk)