Part of acting tough is dealing with physiological and psychological pain. Martial artists deal with physical pain every day. We always have aches and pains, so we learn to train though the pain.
Emotional pain is more difficult to deal with since it interrupts the thinking that we use to maintain physical control, but it must be controlled if we are to be tough when we are dealing with adversity. Even if you are not tough, if you act tough, it may be enough to get you through a stressful time.
Not all martial artists are able to be or act tough. Some can be tough when there is help around, such as enduring an injury during a tournament when friends and medical help are available. However, when they are on their own in the streets with no backup available, they are unable to be tough when facing a criminal. In stressful situations, some even tank and give up.