As it turns out, the exchange of handshakes is a custom that goes back to the times of ancient Greece, more or less in the fifth century BCE. We know this because of the preserved messages and artefacts.
It is therefore natural, that such principles of social life were also present in ancient Rome. We have a large number of preserved reliefs or coins, on which we can see figures giving themselves right hands (so-called dextrarum iunctio). As it turns out, this form of behaviour was mainly ceremonial, which expressed a strong bond between two people, for example between a woman and a man during a wedding, between two entities concluding a settlement, between a patron and a freedman, or simply as a sign of peace and reconciliation.
It is possible, therefore, to suppose that Romans did not give hands in every situation (as we do today), but rather in a more formal moment.
Hollywood films (eg. “Gladiator”) have built and strengthened the view that there was Roman forearm handshake. As we know, such a greeting is much more expressive, carnal and even symbolic. In the opinion of many, such handshake better reflected the character of Romans, in accordance with their principles and loyalty.
We do not have any real evidence (in the form of relief or an ancient source) suggesting that forearm handshake is a typical Roman masculine greeting. It seems that it is rather a later invention, which main aim was to create an aura of perfection around the Romans and their world.