OK, first of all MMA is a Martial Art.
What I believe your friend is trying to say is that other Martial Arts like Karate or Tae Kwon Do are great against each other in a Karate or TKD tournament, but if they were to enter a MMA event and try to utilize just Karate or TKD styles (Striking Styles) against an MMA fighter, who not only knows striking skills but also grappling skills (wrestling, juijitsu) that Karate or TKD fighter would get destroyed. This is true.
In fact, the whole reason the UFC was organized was to pit different styles of Martial Arts together under one roof to see which style would prevail. The Gracie family, who specializes in BJJ (Brazialian Jujitsu), proved to the world that their style at the time was the best suited for open tournaments. They were the ones that actually started up the UFC top showcase their style.
Eventually, strikers learned how to defend against grapplers like the Gracies and grapplers in turned learned how to defend against strikers and thus a hybrid developed which eventually became MMA as we know it.