Luther is a great detective, even though he's quite flawed, but in a way that's understandable, for many of us would have similar issues if we faced what he's faced.
He "knows" a suspect is guilty by how the suspect over-controlled themselves during his "sneeze test" (don't worry, it's revealed right after the sneeze test, so I don't consider that a spoiler). Yet despite the entire team's best efforts, they can't find any real evidence on the suspect, so they have to release the suspect. BTW, the suspect is a genius (natch).
The suspect becomes intrigued by Luther (my guess is that they've never come close to anyone else that's almost as brilliant as they are), and becomes quite involved in his life, and investigations. This is when the show really becomes interesting, especially from the psychological perspective - it's creepy, yet kind of understandable.
I hope there's another season - I want to see what happens after the big showdown!