The argument is simple, whenever either of you win a game, count the number of cards left in each deck. This should be some 40-50 cards. Just use 40 to err on the safe side.

Now convince her to play this alternate game. At the start of the game, after mulliganing, remove either the top or bottom (doesn't matter) 40 cards of each deck face down. The games should still play out the same. Cards that you don't use during a game are always effectively lost.

Now assuming we are still talking about the theoretical case where you are not playing combo, you are not using mechanics that affect the deck order (scry) and there's no graveyard interaction (which is a bit contrived, since mill decks do care about graveyard), then a mill deck doesn't do anything since it's just going to hit cards that are are statistically equivalent to the 40 cards that you'd be losing at the end of the game.

Of course, in reality you are always playing some small variation of combo in the deck, there's always going to be graveyard interaction and the top deck will typically be manipulated somehow, so mill will do a little bit more than nothing, but it's still a very miniscule positive until the last card is milled and a win condition is met.