The following quotes are taken from "Siouxsie And The Banshees: The Authorised Biography", by Mark Paytress, and mainly relate to Juju, which came out in 1981.
Steve Severin: "We'd actually described Join Hands as "gothic" at the time of its release, but journalists hadn't picked up on it. Certainly, at that time we were reading a lot of Edgar Allan Poe and writers like that. A song like "Premature Burial" from that album is certainly gothic in its proper sense.
Phil Oakey: It wasn't the bands fault but I do think they invented goth as we know it. They were archetypally what it became - especially those intense vocals and Kenny's terrific tribal drumming. It established the pattern.
Sioux: I've always thought that one of our greatest strengths was our ability to craft tension in music and subject matter. Juju had a strong identity, which the goth bands that came in our wake tried to mimic, but they simply ended up diluting it. They were using horror as the basis for stupid rock n roll pantomime. There was no sense of tension in their music. Anyway, Juju wasn't all about darkness.
Severin: If there was a band that influenced what we did on Juju, it was The Cramps. Not musically, because they were much more rooted in straightforward rock n roll,but in terms of some of their imagery and the way they came across.
John McGeogh: The Banshees would never call themselves a goth band because it's simply not true. The sound on Juju had more of a rock feel to it and, in some ways, harks back to The Scream. We were always more thiller than horror, that Hitchcockian juxtaposition of two unlikely elements. More blood dripping on a daisy than scary beast sinking its fangs into the victim.[...]
Billy Chainsaw: I never understood why they hated being described as goth. You only have to look at the lyrics, especially some of the stuff that Severin used to write. I'm not talking about bats and ghosts, I'm talking about Gothic literature as an artform. C'mon, the band's name comes from a Hammer horror movie - Cry of the Banshee! That root had always been there. It just happened that a genre came along that later called itself goth. It didn't really matter, because the copycat bands were imitators. Nothing was ever going to be as good as the original.
Sioux: I've always seen these tags of convenience that journalists come up with as lazy journalism and a real cop-out, an inability to deal with something that they can't or won't understand. Call it what you like - punk, funk, new wave, goth, I don't care. I don;'t want anything to do with it. I would never limit myself this way, or use these terms to describe our music. Now if you're talking about people with a flock mentality and a need, that's something else. There are plenty of people like that. We're not liike that. I'm not like that. Juju was an African word for karma or luck. There's good juju and there's bad juju.