Why does time go forward and not backwards? This might seem like a simple question, but it's actually really complicated. Physicist Sean Carroll explains in a video for Minute Physics.
Most of the laws of physics, like gravity and quantum mechanics, are symmetric with respect to time. That means that it doesn't matter whether time moves forward or backwards. If time ran in reverse, all the laws of physics would work the same.
That is, all the laws except one. The Second Law of Thermodynamics does imply a direction. The Second Law states that over time, everything moves from an ordered state to a disordered state. It's the only physical law that can't go backwards.
The Second Law is the reason why you can mix stuff but you can't unmix it, like coffee and cream. Unmixed, they're in an ordered state. Mixed together they are disordered. The Second Law of Thermodynamics says that no matter how hard you try, you can't unmix the coffee and get the cream back out.
The Second Law of Thermodynamics is the reason you can't go back to the past. The universe, like an unmixed cup of coffee, started in an extremely ordered state. Over time, the universe mixed together and became less ordered, like what happens when you stir the coffee. Going back in time is unmixing; it can't be done. The universe can't be 'unmixed'.
What this means, ultimately, is that time only exists because the Big Bang created a universe that started out ordered. If the universe was disordered from the beginning, there would be nothing left to mix and time would not exist. This also means that someday in the far distant future, once everything in the universe gets mixed for good, time will disappear completely.