Who was really the "fizzle bomber" in Predestination?

Question

Who was the fizzle bomber, and how? The film indicates that

Ethan Hawke's charater is, but was he actually the child of two of the same person, one male and one female but the same person?

I don't understand.

Answer 1

The major conceit of the story is that using time travel, Hawke (John) travels backwards in time to a point where he crosses his own timeline and has sex with his mother (Jane), kidnaps their resulting offspring and deposits it in an orphanage so that the baby becomes its own mother.

To complicate matters further, it transpires that his mother is himself (having had a sex change some years after having had her baby) and that due to his/her hermaphroditism, s/he has bred with him/herself.

The resulting offspring is recursively both father and mother as well as its own grandparent infinitely.

Oh, and the Fizzle Bomber is an older John, driven mad by all the time travel. He's also the Barkeep, responsible for recruiting himself into the Time Corp.

In short...

Answer 2

Ref: Predestination Explained

Agent Doe travels back in time to complete his last assignment: recruit their priced asset and prevent the New York bombing. So he traveled back in time, ironically, to recruit himself. Every time he traveled back he has a slight tendency to make a little detour and in his latest rendezvous with time he discovered one very crucial piece of evidence that could lead him to the frizzle Bomber.
As he picked up that piece of evidence he went straight where it leads him and discovered to discovered to his own horror as he stood facing the Frizzled Bomber was none other than himself. Not only was he a progeny of himself, created by the union of Jane and John, he recruited himself, became gent Doe and eventually became the Frizzle Bomber. With every time travel, it eats a part of his sanity finally creating ‘psychotic’ Frizzle Bomber.