Last things first and a big spoiler. In Predestination it is missing the third act of the movie. There is also the biggest storytelling prologue ever. We started pretty negatively, didn't we. Well tell me how to describe Predestination as a movie without spoiling it. It is an awesome time-travel story about a man traveling through time to prevent crimes.
Now lets continue. The biggest spoiler i can write and i will do is that in the end there is no other choice that someone can make. Everything is somehow predetermined and sealed by time. After seeing the movie got me thinking that if she never met that guy she would me less screwed and maybe she would not exist? "Hey man... you know that when you time-travel everything around you shatter, so why bother getting into the car to break everything into the car? Just do it outside in the sunny weather."
Mind-rape to the max and even if this is a smart movie, you have to like time-travel to like Predestination as well. Anyway those subtle hints throughout the movie are awesome. It is also fun to spot during the movie as long as you are not distracted by them so you can enjoy the movie. You either see everything unraveling throughout the movie having your mind blown or you finish the movie and think everything that happened and when you figure it out you have your mind blown.
"The Bartender : It's easier to hate than to love, right? The Unmarried Mother : Yeah. The Bartender : It's easier to destroy something. Kill somebody."
"The Bartender : The one thing that this job has taught me is that truth is stranger than fiction."