I think the reason why I don't consider
Se7en a horror film is probably because, for me, the film is more about the relationship between Freeman and Pitt and their unfolding journey in order to catch the killer, rather than the killer himself.
Yes, there are horror-themed scenes, but we only tend to see the after effects, rather than the acts themselves, and with the killer only featuring in the final acts, I see
Se7en as more of a crime thriller than a horror film.
I think the methods in which the murders are committed infer a horror film, but remove the method of the murders, and you're left with
Midsomer Murders - which isn't horror (horrible, perhaps?
)
Obviously that previous paragraph was a joke, and I completely understand why people see
Se7en as a horror film. There are many films I consider horror that others won't do.
I hate strict categorisation of anything by genre anyway.