Putin has popular support, and there's no evidence that Russians are against the war. This sort of argument is about as intellectually dishonest as saying Trump didn't represent the US. Factually, he did. A small minority fleeing the country isn't evidence that everyone opposes the country's leadership, and most of the anecdotes from Russians are about avoiding personal involvement - the fear is of being drafted into the war.

edit: I know this is an unpopular point, but there is just zero basis for saying that Putin isn't supported by his country. He absolutely is, which makes the situation much more complicated.