I would begin with a brief history of the nature vs nurture argument. I would possibly touch on the so-called 'Crime of the Century' the 1920s Leopold & Loeb case. Although not serial killers, their defence (one of the greatest defences in legal history by Clarence Derrow) is based on the above argument and supports nurture as the most defining factor and which probably saved the pair from the noose. Derrow's closing argument lasted twelve hours and brought the judge to tears at its conclusion.
Personally, I would have been an unshakeable proponent in favour of the 'nurture' argument.
However, modern psychology seems to point very much in support of the nature side.
Never having been to university, written a dissertation of even attended school for even close to half of what I was supposed to, others will definitely offer superior advice :-)