I wash before handling snakes, and after.
Your professor is also incorrect. Washing with non-anti-bacterial soap does reduce the amount of pathogenic bacteria on your hands.
While not completely sterilizing you (which is a bad thing any way) it allows the beneficial bacteria that cover your entire body to out compete the harmful bacteria.
At least that is what is supposed to happen, things like open wounds change the game. Also, some people have higher immunity from disease than others. i.e. farm kids or kids raised around a number of pets.