Yes. The speaker is giving a response that is automatic, habitual, out of reflex (like a knee jerk when a doctor taps below the patella). The nature of that response is dark, jaded, world weary, negative, lacking in hope, faith, optimism, belief in the goodness of life or people. You would predict that he doesn't expect to find any key to the meaning of life.

Yes, I think you got the correct gist of it! To further clarify, in this example the term "reflexively" indicates that the speaker gave his/her cynical response without truly thinking deeply about the matter at hand, but rather just as a "reflex". Cynical: not believing anything good about *human nature*. Reflexively: adverbial form of reflex