Q:

Why do the major and minor groove exist in DNA?

So I know that the major/minor groove arise from the offset pairing of the two strands in the helix.  All my textbook tells me is that "pitch causes the off-set pairing of DNA and this gives rise to the major and minor grooves."
I'm not too sure what this is saying.  What exactly is pitch and how does it give rise to the grooves?

A:

Pitch is not a great word for this, as its meaning is ambiguous. It's hard to find a universal nomenclature for DNA geometry, but see the "Base pair geometry" section of this wikipedia page. The relevant property is what they call "opening".
From the biochemistry textbook by Berg:

To explain in words, if the glycosidic bonds (which attach the nucleic base to the sugar in the backbone) stuck straight out at 90 angles on both sides, then the grooves in double-stranded DNA would be symmetrical. Because the glycosidic bonds are at an angle (relative to the interface between the AT or GC pairs), one of the "faces" of the base pair is larger than the other.
Words and flat pictures, however, will never really give you a good intuitive sense of what's going on with the 3D structure of the grooves. A good modeling kit will be of great help to you.

