In this work, we consider the area non-increasing map between manifolds with positive curvature. By exploring the strong maximum principle along the graphical mean curvature flow, we show that an area non-increasing map between positively curved manifolds is either homotopy trivial, Riemannian submersion, local isometry or isometric immersion. This confirm the speculation of Tsai-Tsui-Wang. We also use Brendle's sphere Theorem and mean curvature flow coupled with Ricci flow to establish related results on manifolds with positive 1-isotropic curvature. 