[lolc]

> In chess, you have to make mistakes to lose.

That's a conjecture. Nothing more. Nobody knows whether it is true! It is possible that a perfect player playing White may make you lose every time. It's even possible (though highly doubtful) that this holds for Black instead.

[umanwizard]

You're right that in theory nobody has proven whether chess is won, lost, or drawn with perfect play. But all available evidence, as well as my personal intuition (and that of almost all top players), screams that it's drawn.