1. to refuse to accept that something is valuable or important
you can't brush off citizens' concerns
When you 'brush something off', you dismiss it as not being valuable or important and refuse to treat it with the importance it deserves. Usually you 'brush something off' when you are in danger of feeling the ill effects or consequences of recognising what has happened or what has been said. For this reason, to 'brush off' has a negative connotation. You might also say that someone gave you 'the brush-off' if you think they dismissed you unfairly.