You are halfway correct. The game is indeed binary. A property is either liked or disliked by the user, and the player has to deduce which is which.
However, the profiles at the bottom-left are just suggestions for the user. The player has to see which one matches with the user, which one does not, and why. With that, the player can see what the profiles have in common and can deduce what the user likes or dislikes.
Hope it’s a bit clearer !