Just becuase no one has figured out a way to time travel does not mean the it is impossible. History should tell you that. As for time machines being built, that would be a matter of who you want to believe. I believe it possible but dangerous, just from the machinical point of view. Stabilty at a high energy is not that easy.
On occations, I have attempted to recreate the experiments of others and have tried my own as well. So far I have had no success. If time travel is possible, it is probably much to complicated for the average person to build in his or her garage.
This universe is full of mysteries, we never know and we can not tell if something is possible or something is impossible. Our knowledge is limited to some extend, so, we should leave some exemptions in everything. Throughout the man kind histories, there are so many myths, can you know if these myths are true or fake? You can never tell