Here is what I think.
Lets say there is a terrorist attack on a train car. There are 12 people on that train car and they all die.
Lets say that someone goes back in time and stops that from happening... now there are a infinite number of possibilities that can occur, but here is one that I am going to give as an example.
One of the passengers that are now alive because they prevented the terrorist attack, we will call him Joe, meets a young woman, we will call her Jill. Joe and Jill fall in love and get married. They have 6 children... Great everything went well, then comes along Sarah, James, Adam, and Rebecca from this line and they meet people and fall in love and get married. Then Hitler, Manson, Bundy, and Gangus Kung are all reborn and they cause the apocolypse. Now if Joe had died in the terrorist attack like he was suppose to have, then the new Hitler would not have ever been born. I know it is all a bit far fetched, but you get the jest of what I am trying to say.
When you start messing with time, there are so many bad things that can come with the good. You may stop one bad thing but there are a number of horrible things that can come as a result of it.