If you've decided to have the Earth destroyed, then you clearly already have your motive and don't need my advice. But if, for whatever reason, you're seeking to get inside the mind of the planet-killer, then read on.
A response first given by George Mallory after being relentlessly questioned as to why he desired to become the first man to climb to the highest point on Earth, the peak of Mount Everest. It did for him and it can do for you. Who needs a reason? The doing of the thing is its own reward.
You'll be employing the scientific principles of [whatever method you use] on a greater scale than ever before. You'll have recording devices observing the event from all angles and on all wavelengths. The telemetry taken from the destruction of the Earth will reveal more about the universe, and science, and the Earth itself than anybody can possibly imagine! Isn't that worth it?
One can't argue with the fact that the total annihilation of an object of the Earth's size is going to be pretty spectacular however it happens. If you are the kind of person who likes explosions and implosions and other destructive events, then this is going to be the biggest you're likely to experience in a lifetime.
If you can destroy the Earth at relatively minimal cost and in an extremely short space of time - short enough, that is, that nobody can escape after they see the death-blow coming - then these might be valid motivations. Humanity threatening your stranglehold over every planet in the galaxy? Humanity GOT a stranglehold over what you believe should be a free galaxy? Just not much of a people person? Job done.
Obviously this is huge overkill: but if you're evil, that's part of the business.
Should definitely keep the other misbehaving border worlds in line.
Can I just point out here that this is a singularly stupid reason to destroy a whole planet. As viewed from Mars, both the Earth and Venus are absolutely tiny. Not only is it highly unlikely that all three would EVER line up so perfectly that the Earth obstructs Venus, after a few hours they would have moved apart and Venus would be clearly visible again.
Surely a hyperspace bypass would pass through hyperspace, not reality?
Earth is old and obviously in pain; it should be put out of its misery.
Anything along the lines of "They laughed at me at the Academy, I'll show them, I'll show them all!!" would fall under this category, though it could also be pegged as a psychological reason, below.
"Hate world, world hates me" would fall under this category. So would insanity.
Religion is regarded by many as the most dangerous weapon of any kind. Certainly its damaging effects on human history cannot be overstated. People will do anything, anything, up to and including the torture and murder of millions of people if they sincerely believe, however misguidedly, that whatever deity or deities they believe in are on their side.
It doesn't matter if you really believe God wants you to destroy the Earth. If your minions buy it, they may never be stopped, even after you're long dead. Faith is powerful.
Obviously there's a limit to how big an accident can get. Clearly one cannot steer many tiny asteroids on fly-by passes of Earth and carefully move it out of orbit and off sailing into Jupiter by accident. But perhaps some horrible scientific accident could set off a rapidly expanding true vaccuum decay zone kinda thing, or worse. Or maybe you could try to steer the Earth past the Sun, and get your numbers slightly wrong, or have a rocket fail on you. Be creative and the kinds of accidents I'm talking about here seem more and more plausible.
Still. Pretty difficult to make an accident this big.
I can only guess at what sort of situation would require the Earth to be sacrificed, but you know, if it arose, who could say no?
One suggestion is: prophylaxis. If the Earth becomes contaminated with some agent - a virus, perhaps, either biological or technological (i.e. grey goo nightmare) - and that agent threatens other worlds, then it may prove that the only way to wipe the threat out permanently is to destroy the Earth with it.
This is probably the most plausible reason on this list. It's fine, of course, to destroy such a useful planet if you're planning to render the material thus liberated into a more useful form - for example, part of a Ringworld, or many, many Banksian Culture Orbitals, or still more Halos, or unimaginable quantities of smaller space-going habitats. A Culture Orbital, for example, is a fourteen-million-kilometre-wide spinning ring, with people living on the inside edge, held there by centripetal acceleration. Its habitable surface area is immensely more than that of Earth, but the material required to create one is much, much less than that needed to make a whole planet. You could trade the Earth for millions or billions of times as much room. Fair? I think so.
There are of course much more convincing arguments for NOT destroying the Earth. These include:
...and expensive, and time-consuming, and have relatively little payoff. What's the point? Why bother?
Earth is an important wildlife reserve. It contains samples of an amazing number of different species of animal. To destroy the Earth would be to render extinct all of these species.
Earth contains huge amounts of unique habitat. There is nowhere else in the known universe that e.g. humans can live comfortably.
Earth also has vast untapped resources of air, water, and minerals.
This is where a lot of us grew up, after all.
Murder and property destruction would be the most prominent charges brought against you in the aftermath.
Personally I believe that the arguments against geocide, though limited in scope, are convincing. I don't want Earth destroyed anytime soon - I'm just having too much fun with it still existing. Still, everyone's entitled to their own opinion. What's yours, and how did you arrive at it? Email me.