Well, there's been some alarmism about AI recently, and in that same vein I'll admit it - even with a physics degree I'm uneasy about the LHC. By definition we don't know what will happen. We are generating kinetic energies that haven't been seen since literally the dawn of time. I would just be a lot more comfortable if these experiments were being done in space, far away from life. It's just that even 99.999% certainty that nothing catastrophic will happen really isn't high enough considering the stakes.
On the one hand, yes. There should always be a healthy concern for safety.
But keep in mind these sorts of things happen relatively frequently - https://en.wikipedia.org/wiki/Oh-My-God_particle Furthermore, they have a really good idea of what's going to happen. With bowling, I can't tell you if i'm going to roll a strike or a split, but i'm sure i won't hit you with a bowling ball.
To put it another way, if there was some scary possible outcome, there would be evidence of that from the many particles that hit us regularly. Mini black holes sound scary, but they're really tiny and just evaporate because they're, well, mini. Nuclear reactions are well understood. If there was some other effect, we'd see it in the sun. Just think about how hard it is to get fusion power working. What are the chances of that happening accidentally?
So yes. You and I are right to be concerned, we're facing the unknown. But if you look into it, you'll see the folks doing the research, well, it's not unknown to them. They're looking for small details in well understood systems. Maybe something bad will happen, but they're not shooting from the hip.
Re: "We are generating kinetic energies that haven't been seen since literally the dawn of time."
Is 13 TeV really considered a lot of energy in terms of what happens daily with particles hitting our atmosphere? http://en.wikipedia.org/wiki/Cosmic_ray seems to suggest that we've observed naturally occurring 3 × 10^20 eV, which is a lot ( larger than 13 TeV (10^12).
You have to look at center of mass energy, the energy actually available for reactions in a collision. The collisions of ultra-high-energy-cosmic-rays (UHECRs) with air occur at hundreds of TeV center of mass energy. And they may be nucleons, in which case this energy is spread over several nuclei. So assuming that Lorentz symmetry holds (probably the safest assumption in modern physics), 13 TeV is in a similar ball park as UHECR collisions.
> For the Oh-My-God particle, this gives 7.5×10^14 eV, roughly 50 times the collision energy of the Large Hadron Collider.
> The speed of the particle (0.999 999 999 999 999 999 999 9951c), if it was a proton, is so high that it would experience relativistic time dilation by a factor of about 320 billion. At that rate, the particle could have traveled for the entire duration of the universe's existence while experiencing less than sixteen days subjective time.
EDIT: add 'kinetic'