Lots of people hitting the target but no one hit the bulls-eye yet, so here goes...
TENEBRE is Argento's best - and one of the best horror films ever - not because it is non-linear or an experience, but because it is anti-linear, a structural device used to undermine our comfortable sense of a rational world in which things make sense.
The film deliberately evokes old-fashioned amateur detective stories in which the writer of mystery fiction matches wits (and usually outwits) the official police force. There are also direct references to the Sherlock Homes stories, in which any incredible mystery could be solved with enough brain power.
Having set all this up in the first half, the film deliberately blows it to pieces in the second half by introducing all the wild and crazy Argento stuff his fans have come to crave. The intrusion of the near irrelevant set-pieces (like the girl chased by the dog who eventually wanders into the killer's lair by accident) undermine the logical structure of the film.
This leads to the conclusion, in which the traditional detective methods fail to identify the killer because the killer's behavior does not conform to any rational concept: he left his ex-wife and yet he kills her and her lover, theoretically out of jealousy but really because he is reliving an old nightmare of having been sexually humiliated on the beach by a young woman who shoved that wonderful phallic red stilletto heel down his throat.
All this ties in with the self-reflexive nature of the movie. TENEBRE is about a book called "Tenebre" that inspires a reader to act out the horrors described therein. In effect, the film is saying that society's worst fears about the horror genre are true. Fear comes not from identifying with the film's characters and wondering if they will survive but from the cynical message being purveyed, in which we are supposed to wonder whether filmmaker Dario Argento and his ficitonal counterpart, mystery writer Peter Neal, are not too close for comfort.
Read more here
http://hollywoodgothique.com/tenebre1982.html