Writing to Christians in Corinth St. Paul told said, “Clear out the old yeast. For our Paschal Lamb, Christ, has been sacrificed.”
The old yeast is a metaphor for such un-Christian attitudes as greed, lust and pride; and the basis for the metaphor dates back to the flight of the Israelites from Egypt.
Moses and the Israelites sat down for that final meal in Egypt. Then, when they had consumed the Paschal lamb, they threw together the ingredients they would need for eating on the road. Since they would not have an opportunity for baking, they would need no yeast, so they got rid of the old yeast. As well, they disposed of barley and some other ingredients. Those were the condiments and foods they wouldn’t be able to use on the long walk to Mount Sinai. Those foods they disposed of make up the list of non-kosher foods that devout Jews still do not eat.
Jesus pointed out other metaphorical meanings for yeast. In telling us to avoid the yeast of the Pharisees he was telling us to avoid the pride that puffs people up the way yeast puffs up dough.
Jesus metaphorically used the beneficial aspects of yeast in saying that instead of isolating themselves from the world’s masses, Christians should be like yeast, mixing with discouraged people, lifting them up.