Time travel exists and has been proven by multiple confessions. It is the phenomenon most commonly noticed after your alarm goes off. You close yours eyes for less than a second and boom. You're 30 minutes into the future. This is an inexplicable design error that was implemented by our creators. Otherwise known as a bug that got left in because it was interesting.
Now jokes aside, if time travel is ever invented, we would never realize it unless we personally traveled. That is because once a person goes back in time, just by being there, he has changed the future. No matter small the difference, the future would be a different one. Due this most people like to believe the idea of alternate timelines. This is the concept where each change causes a new separate timeline to form. There would then be the original one and a new one. The time traveler would definitely not be able to return to his original timeline. And if you go forward in time, you would create a timeline where you mysteriously disappeared. Most would then credit this to the work of aliens or a kidnapping. Your friends and family would also grieve. Thus the mere thought of time traveling is kind of taboo.