be under the illusion that

To be living, operating, or functioning based on a belief that is fanciful, unrealistic, or untrue. Jeremy's always been under the illusion that he's a great writer, even though he's never written more than a few crummy poems. No one likes paying taxes, but those who would call for them to be done away with altogether are under the illusion that our society can function without them. I'm not under the illusion that my kids are angels, but I never expected them to lie to my face about sneaking out.

be under the illusion that

wrongly believe that.

1998 Independent The keening harmonies of the Brothers Gibb, a million naff dance routines by medallion men under the illusion that they were John Travolta.