Start with the standard scenario: trolley speeding towards five innocent strangers, and you can flip a lever to redirect it to a side-track with only one innocent stranger. Here are four arguments each making it plausible that redirecting the trolley is right. [Unfortunately, as you can see from the comments, the first three arguments, at least, are very weak. - ARP]
1. Back and forth: Suppose there is just enough time to flip the lever to redirect and then flip it back--but no more time than that. Assuming one shouldn't redirect, there is nothing wrong with flipping the lever if one has a firm plan to flip it back immediately. After all, nobody is harmed by such a there-and-back movement. The action may seem flippant (pun not intended--I just can't think of a better term), but we could suppose that there is good reason for it (maybe it cures a terrible pain in your arm). But now suppose that you're half-way through this action. You've flipped the lever. The trolley is now speeding towards the one innocent. At this point it is clearly wrong for you to flip it back: everyone agrees that a trolley speeding towards one innocent stranger can't be redirected towards five. This seems paradoxical: the compound action would be permissible, but you'd be obligated to stop half way through. If redirecting the trolley is the right thing to do, we can block the paradox by saying that it's wrong to flip it there and back, because it is your duty to flip it there.
2. Undoing. If you can undo a wrong action, getting everything back to the status quo ante, you probably should. So if it's wrong to flip the lever, then if you've flipped the lever, you probably should flip it back, to undo the action. But flipping it back is uncontroversially wrong. So, probably, flipping the lever isn't wrong.
3. Advice and prevention. Typically, it's permissible to dissuade people who are resolved on a wrong action. But if someone is set on flipping the lever, it's wrong to dissuade her. For once she is resolved on flipping the lever, it is the one person on the side-track who is set to die, and so dissuading the person from flipping the lever redirects death onto the five again. But it's clearly wrong to redirect death onto the five. So, probably, flipping the lever isn't wrong. Similarly, typically one should prevent wrongdoing. But to prevent the flipping of the lever is to redirect the danger onto the five, and that's wrong.
4. Advice and prevention (reversed). The trolley is speeding towards the side-track with one person, and you see someone about to redirect the trolley onto the main track with five persons. Clearly you should try to talk the person out of it. But talking her out of it redirects death from the five innocents to the one. Hence it's right to engage in such redirection. Similarly, it's clear that if you can physical prevent the person from redirecting the trolley onto the main track, you should. But that's redirection of danger from five to one.