When the piece of paper is dangled, they become two individual papers having some distance between them. As per Bernoulli’s principle, when the wind blows from these two pieces, the pressure between them will decrease.
The pressure in another environment of the paper remains the same. As the pressure between them decreases, it creates a pressure difference between the papers and surroundings.
This pressure difference tends the two pieces of paper to move towards each other to balance the pressure difference between the surroundings. Therefore, the two pieces will move inwards when the wind blows through them.