One of the ways in which Ancient Sumer was not egalitarian was the government by a monarchy. The early civilizations had many new things that they must get used to. One example of this was that they would have needed someone to govern them and tell them what was right and wrong. Another was that the farmers in these ancient civilizations were that they needed to know when they could farm. If they were not able to ask someone to do so, all of the farmer's crops would fail and there would be no harvest and no one would be able to eat and starve.
Later on, the kings said that they were gods and the people should respect him. The kings were usually given the throne by family. This meaning that the king had the most connections between the families that were living there at that time. This was also another non-egalitarian feature of ancient Sumer.
Another non-egalitarian feature is the lower ranking people had to show deference to the people who ranked higher than they did. Some of these "high ranking" officials would be people who were nobles or priests. The nobles promised the farmers that if they provided the nobles with food, that they would serve them in return by protecting them from various things such as bandits, and other human enemies. Priests in return they said that they were what stood between the humans and the gods. The priests said that if the farmers provided them with food, they would protect them from the supernatural enemies.
Also the laws that they had were held by the king. This most likely meant that the kings were the judges of the time that they ruled in. The kings probably ruled whatever he wished, not bothering to gather enough evidence to prove the case's liability. Even though the law the there was called lex talionis, this could not prove that the person who was convicted really did it.
Although lex talionis dealt with everybody's losses, it didn't dealt with the nobles correctly.