Of Fire and Brimstone
The Satanic Cross was originally the symbol for the element which was called brimstone in antiquity, and which we today know as sulfur. The association of sulfur with Satanism is rather dated, and has its origins in its use as the symbol for sulfur by European alchemists.
It was one of the three special elements alchemists added to the classic Aristotelian system, with the other two being salt and Hydrargum or Quicksilver, which we now call Mercury.
Brimstone is found naturally as a pale yellow solid which is brittle and odorless. In its natural solid (as a block or as a powder) form, sulfur does not react with air. However, when exposed to a flame, it burns in a way that is quite unlike any other element that we know.
The general way people see things is that if a symbol is inverted, the resulting shape must indicate the opposite of the original meaning. On the surface, that is entirely logical and we see this belief at work in the paired representation of many ancient symbols.
Water is depicted by a triangle with its single vertex pointing up, while the complimentary element, fire, is depicted as a triangle with the vertex pointing down. In eastern tradition, the symbol of the male and female, the yin and the yang, are complimentary shapes, too.
By that logic, inverting the cross, we would get the symbol of the opposite of Jesus or God – Satan. That is perhaps the way Anton LaVey, founder of the Church of Satan envisioned things when he adopted the Leviathan Cross as the symbol of his Church.