Jesus got up at the passover meal to wash his disciples feet. By doing the job of a servant, he was demonstrating that he came to be a servant and wash the world of their sins. Only Jesus can offer us that forgiveness!
Nobody wants to be a slave. When somebody–or something–is controlling you it becomes difficult to be who God called you to be. God promised that the Israelites would be his chosen nation, but they were enslaved by the Egyptians. By the blood of a pure and spotless lamb, God spared his people from the devastation of the final plague, and he set them free from slavery. Jesus cares about the whole world enough that he came as the pure and spotless lamb so that we could be set free from sin.