Okay, here it goes...
Scientist guy has a fiance. They are mugged- she is killed. He spends the next several years (decade?) inventing a time machine so he can go back and change it. He builds it, he goes back. He finds her before the mugging and takes her away from the park where it happens. After he distracts her for a while, he decides the mugging has been averted so he prepares to leave and go back to his own time. He walks away, and she gets run over by a run away cart and is crushed to death. He realizes that he can change the circumstances, but not the outcome of her death. (Movie makers potentially should have had one more attempt at doing this (or a montage!) because I doubt he would have concluded this without further attempts) He doesn't know WHY he can't change the past- simply he knows that he can't. He decides that maybe they know in the future why you can't change the past... so he goes forward in time and finds the height of society and scientific understanding. They don't know so he gets in the timemachine and ends up a quadrillion years in the future with the Morlocks and the Eloi. This is the part of the movie that sucks, IMHO. He eventually talks to the leader of the Morlocks who has stolen the time machine and wants to use it for AWESOME (I mean EVIL). He tells the timetraveler why he couldn't change the past:
Actually you can change the past. BUT you can only change it in ways that don't create paradoxes. Since the time traveler was only ever motivated to invent time travel to avert the death of his fiance... that event MUST ALWAYS occur or else he wouldn't have created the time machine with which he changes time.
As in Warbler's Terminator example... if Skynet invented Time Travel with the sole purpose of undoing its defeat at the hands of the adult John Connor, their change to the timestream (killing Connor) would create a new timeline where they aren't defeated and therefore have no reason to invent time travel. Therefore it is not invented, and they don't change time so they are defeated by Connor so they do create time travel, so they aren't defeated by Connor, so they have no reason to invent time travel, so it is not invented, and they don't change time so they are defeated by Connor so they do create time travel, so they aren't defeated by Connor, so they have no reason to invent time travel, so it is not invented, and they don't change time so they are defeated by Connor so they do create time travel, so they aren't defeated by Connor, so they have no reason to invent time travel, so it is not invented, and they don't change time so they are defeated by Connor so they do create time travel, so they aren't defeated by Connor, so they have no reason to invent time travel, so it is not invented, and they don't change time so they are defeated by Connor so they do create time travel, so they aren't defeated by Connor, so they have no reason to invent time travel, so it is not invented, and they don't change time so they are defeated by Connor so they do create time travel, so they aren't defeated by Connor, so they have no reason to invent time travel, so it is not invented...
MY HEAD ASPLODE!
So, in conclusion, the one thing you really want to change in the past is the one thing you can't change. Really, you can probably only change things by accident. So, going back to the past sort of sucks.
OR
B. Invent a time machine now so you'll have it BEFORE you need it.
I shall go with B. See you in a few thousand years, suckers!