The "when, where, why" of language origins, a most interesting and, at the same time, frustrating question. You won't find many serious linguists who will touch the subject with a ten foot pole. I find everyone's comments very interesting here, and I really hesitate to enter the fray, since I really know nothing about origins, despite a long history in linguistics. But I have my guesses.
My experience has been that "origins" was a taboo topic much like "cold fusion" is for physicists. There are no data, and there possibly never will be.
Natural language, I still believe, has its innate components, as well as its superficial or external evidences such as production, phonetics, morphology and syntax. Language is frustratingly societal, intellectual, psychological, and physical, all at the same time. I find that very few in the academic world have a proper appreciation for the immense complexity of theoretical syntax and semantics, and few can see the beauty of phonology, let alone morphology except for those who have studied the matter extensively. This tells me that at its deepest roots, human language has to be so incredibly simple in principle as to make us blush, or no one could possibly learn to speak, but it is not an easy nut to crack. The subject really reminds of Feynman's remark about quantum physics. If you think you understand natural languages, you don't....
In order to discover "when it arose", may entail "why" it arose. I suspect language is chosen for by selection, out of necessity for activities like hunting, manipulation of fire for sure, tool making, and sexual rituals. As someone mentioned earlier, the physical mechanisms must also be in place for production of the sounds needed for speech. Perhaps there will be a hint in fossilized remains as to the presence of a proper
hyoid bone, that could give some measure of proof of age. Language also was likely a preparation for bipedalism as well, shouting long distance messages while standing and/or running.
It certainly is a fun topic to theorize about.