Why do we say break a leg?

The urbane Irish nationalist Robert Wilson Lynd published an article, “A Defence of Superstition”, in the 1 October 1921 edition of the New Statesman, a British liberal political and cultural magazine, regarding the theatre as the second-most superstitious institution in England, after horse racing.
In horse racing, Lynd asserted that to wish a man luck is considered unlucky and so “You should say something insulting such as, ‘May you break your leg!’ Thus, the expression could reflect a now forgotten superstition (perhaps a theatrical superstition, though Lynd’s 1921 mention is non-theatrical) in which directly wishing a person “good luck” would be considered bad luck, therefore an alternative way of wishing luck was employed.
Lynd did not attribute the phrase in any way to theatre people, but he was familiar with many of them and frequently mingled with actors backstage.