It's just insanely illogical. There's no logic to it. At all. It's just "Well...we'll do this to make the story work".
Like I said, if the movie wasn't so serious, I wouldn't care, because almost no one gets time travel right anyway, but this movie took itself VERY seriously and therefore I was let down they put so little thought into the time travel logic. Might as well have added in that we only use 10% of our brain and whatever.
I mean, if you like it, cool, more power to you. But please don't tell me my reason for disagreeing with their logic is wrong.
I'll give an example with the ending, since it's the one I remember best, sorry for spoilers.
Little Willis shoots himself to stop big Willis from killing the mom. The logic being that if little Willis is dead, big Willis never existed and therefore disappears. However, that makes no sense. If little Willis dies, and you're saying big Willis never existed, then he never went back in time in the first place because he never existed, he never caused the entire plot to happen. If you want to say that you can actively re-write the timeline, then it wouldn't magically only take affect at the dramatically important time.
That remake movie of The Time Machine explained it pretty well. Dude keeps trying to go back and change his past but can't do it no matter how he tries. Eventually he finds out that if he goes back in time to change the past, then he never has a desire to go back in the first place, because the past no longer needs changing, and therefore never goes back to change the past. It's a paradox. This movie just ignored it and went with the most lazy way with it.