Why Doesn't More People Believe In The Sixth Sense?

Nothing is beyond science. Science is the very definition of the way things work, it encompasses all possible reality. If magic were real, it would be science, as it would fit into some sort of system. If there was any scientific proof, rational people would believe in it. But they don't because there isn't. There are many possible expanations for what you describe as a sixth sense here, but I won't go into them.