The brain does want to predict (in fact I think that's what it's suppose to do), the problem is that the Earth is rather chaotic and unpredictable.
If you subject a brain-like neural network to watch planets and stars orbiting around each other and rewarding it for getting things right, it will likely do quite well.
Not that kind of predict. And this reverse-time brain instantly forgets things it saw for the last time.
Consider a black box. A person opens it, sees a dice with a number, closes it. In our version of the time flow, the person finds out there's a dice and remembers it. In the 'reverse time' persons brain, they would know they would open the black box and know which number they will see. Then they will close it and completely forget what was inside forever.