Caves are usually filled with strange gasses like sulfur dioxide. He's crying because the sulfur dioxide is dissolving in the moisture of his eyes to form sulfuric acid(hence the tears)...just like chopping a onion. All that emotional crap is just a facade.
Oh, so why aren't the two Uchiha's crying? Who can handle more eye burning than people who bleed from their eyes on an occasional basis? No one in the manga(except Ichiraku...cause he's a chef. Duhhh!!).