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.
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.