Despite what some dance teachers may tell you, the clave rhythm is not a factor in most of the music to which you dance your modern International Latin syllabus. It is scarcely a shadow of its original self, not the entire driving force behind the rhythms played by the entire band, as it is in more traditional forms of Afro Cuban music. Most Rumba and Cha Cha music played at your dance studio may contain some small nod to clave, often played by the rather high-pitched and insignificant clave instrument, which when not being backed up by the rest of the band, provides no real driving force of its own -- just a light and barely noticeable accent. In other words, it would be nothing that would make you feel inclined to follow anything other than the instruments all playing together, which is to say the natural agogic stress of the basic 4/4 structure, i.e. strong beats being 1 and 3.
Your Latin dance teacher may give you any number of reasons why he thinks you should break on beat 2. Perhaps he'll say it's the clave, or maybe he'll spout off something about the hip shift after the side step being the "strongest" action. Whatever the justification, the truth is, nobody really knows exactly how it came to be that we all must break on 2, and so everybody just parrots the explanation(s) they heard from their teachers. It doesn't matter whether it actually *is* more musical -- the truth is, it isn't -- what maters is that that's the way it's been done for several generations. And when you've spent a career dancing a particular rhythm (or even just a few months), your brain will accept it as the best rhythm.
At any rate, you're correct. The clave rhythm is irrelevant to us as modern studio-trained Latin dancers. But if you're interested in studying it, you'll find no shortage of information about it on Google, in book stores, and in music stores near you. It's a fascinating topic. Just don't expect to get very much reliable information on the subject from ballroom dancers.
Regards,
Jonathan Atkinson
www.ballroomdancers.com