Master Bo' Rai Cho has been around for centuries. He's trained the likes of Liu Kang, Kung Lao, centuries earlier, in the 1600's, he trained Musō Gonnosuke Katsuyoshi, and even centuries before that he trained The Great Kung Lao (according to Kung Lao's MK 2011 ending). We aren't told precisely how old Bo' Rai Cho is, but only that he's trained many of Earthrealm's greatest warriors and participants in the Mortal Kombat Tournament for ages. We know that he didn't fight for Outworld because his having been born there would mean his, almost assured, victories would count for Outworld. This raises two important questions that are as yet unanswered.
First, how did Bo' Rai Cho avoid being forced to compete on the side of Outworld? Even for all his skill and prowess, surely Master Bo' Rai Cho could not have dared to openly oppose Shao Kahn. So why did the emperor not chose to sent Bo' Rai Cho alongside Shang Tsung? It is possible that during his first mission to Earthrealm, Kahn thought it too important a task to give to someone other than a trusted advisor like Tsung. Also, Bo' Rai Cho appears to have no working knowledge of sorcery, which was a vital part of the emperor's original plan. We don't know if Kahn or Tsung were aware that Bo' Rai Cho had trained the Great Kung Lao, but it if they did, it makes sense not to take him on the second trip as the Master might simply allow Lao to defeat him. This leads me to believe a big reason Bo' Rai Cho was never forced to compete for Outworld is that it was believed he'd throw the Tournament on purpose. Another possibility is that the true measure of his skills was unknown to Outworld. After all, he trained Earthrealm warriors exclusively, and in secret.
Second, why did Bo' Rai Cho turn his back on his home realm? What happened that made him despise his emperor and realm so much that he chose to aid the enemy. Or, alternatively, what happened that made him love and desire to help Earthrealm? Alcohol may have had something to do with it, or perhaps his alcoholism is another symptom of the same underlying cause. Was his master or a loved one killed in some tragic event behind which was the emperor and/or Shang Tsung? Did he fall in love with someone or something on Earthream only to see them brought to ruin by the Tournament? The possibilities are multitudinous.