Why does time only run forwards?

There's egg on your face, literally. You tried to juggle some eggs, it all went wrong, and now you've got to shower and change your clothes. Wouldn't it be faster to just un-break the egg? Breaking it only took a few seconds, so why not do that again, but in reverse? Just reassemble the shell and throw the yolk and the white back inside. You'd have a clean face, clean clothes, and no yolk in your hair, like nothing ever happened. Sounds ridiculous — but why? Why, exactly, is it impossible to un-break an egg? It isn't. There's no fundamental law of nature that prevents us from un-breaking eggs. In fact, physics says that any event in our day-to-day lives could happen in reverse, at any time. So why can't we un-break eggs, or un-burn matches, or even un-sprain an ankle?
 Why don't things happen in reverse all the time?
 Why does the future look different from the past at all?
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