The truth is LHC does create these kind of cosmic rays, but the Universe as a whole conducts more than 10 million million LHC-like experiments per second, and its still exists!

"The Organization shall provide for collaboration among European States in nuclear research of a pure scientific and fundamental character (...). The Organization shall have no concern with work for military requirements and the results of its experimental and theoretical work shall be published or otherwise made generally available". - this is what CERN primarily states. For what CERN exist are 4 words: Research, technology, collaboration, education.

If you are interested in you can find some more information about CERN in the Extra menu.