Even though the four founders got along well for a time, shortly after founding the school, Slytherin had a falling out with the other founders about blood purity and wanted to accept only pure-blood students. He thought that pure-blooded students deserved to learn magic, and others such as Muggle-borns and half-bloods were not worthy. The other three all disagreed. Most especially, Gryffindor.  

    Slytherin decided to leave the school, but not before secretly building the Chamber of Secrets. He said that only his own heir would open it once they arrived at the school, and they would unleash a murderous basilli living inside to rid the school of all it's Muggle-born students. Even though the founders of Hogwarts were in charge of the school during their time, neither of them were called the headmaster or headmistress of the school. That name was used a little while after Slytherin left, and held by another wizard who was entrusted with the Hogwarts Castle after the three remaining founders passed away.