From the biochemistry textbook by Berg:

![enter image description here][1]

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.

Really this is the kind of thing that you're never going to understand intuitively without a [good modeling kit](http://www.amazon.com/KNEX-Education-DNA-Replications-Transcription/dp/B000O8Z7UQ).

  [1]: https://i.sstatic.net/9KgFS.jpg