Oliver has ripped holes in time and shredded the Standard Line of Agreement fleeing and searching for Neve.
The head of the Time Council views him as the biggest threat ever to their way of life and calls for his execution. While Oliver languishes in time prison, he is given a choice - train to join the Time Core or stay in prison and rot and possibly be executed. If he joins the Time Core it could be years before he can resume the search for Neve.
In spite of her total deletion he cannot give up on her - she must be somewhere out there. If he stays in prison, Rougies might break him out, but it has never been done before.
Either choice takes him further from his ultimate goal.