Egalitarianism is an ideal, never has a society achieved true equality for all. Some societies are notably more equal than others (e.g. social mobility and civil rights are among some examples which are extended under this principle). In a sense though, Athens was remarkably egalitarian compared to contemporaneous cities: 

• “[…]the enduring cooperation between citizens and non-citizens in Athenian business life – the recognition of which surely weakens the plausibility of a rigid demarcation line having supposedly physically segregated the various legal status groups – had important implications for the scope of social mobility in Athenian society”

1) Commercial transactions between citizens and non-citizens were prevalent.

2) Interactions in the democratic, free space known as the ‘agora’ are symbolic of a society where class rigidity and subsequent plutocracy do not dominate.

The point: Yes, Ancient Athens had a class system that included slaves and is therefore not egalitarian in a strict sense. But social mobility existed in society, meaning that Athens had developed both institutions and social conventions that embraced the principle of egalitarianism.

Source: Marloes, Deene. 2014. “LET’S WORK TOGETHER! ECONOMIC COOPERATION, SOCIAL CAPITAL, AND CHANCES OF SOCIAL MOBILITY IN CLASSICAL ATHENS.” Greece and Rome 152-160.