The History Channel makes compelling arguments for how extra-terrestrials built the pyramids. Compelling doesn't always equal true.

Sure, but something can be "compelling" for any number of reasons and truth or accuracy don't need to factor in. People like to hear what makes them feel good or confirms their existing beliefs.

In much the same way that meth is "compelling"

Enticing arguments. The rightwing media gives an enticing view of the world, to a certain demographic. Compelling would be more if we saw people from all walks of life being convinced.

Or, and I know this is really out there, but maybe, just maybe, facts don't actually care about your feelings.

this material contains compelling arguments

Maybe for idiots