I've been pondering on the fact of social hierarchy in any given society, that is, as Rousseau says it in his famous 'discourse of inequality', that the individuals are different based on what position they have in a society, making it a class society. A hierarchy based on the demand of different types of work.
I guess my question is: how does anarchist theory respond to this type of hierarchy?
I’m sorry if you find some ambiguity or wrong spelling in my entreaty, English isn't my maternal language.



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I think there are two or three concepts being discussed here all of which are under the term 'hierarchy'. that's not your fault though and loads of people with English as their first language get them mixed up as well.
Social status: the public 'worth' alloted to different occupations, which doesn't necessarily correlate with income or authority. Nurses vs. lawyers for example. I think this is a result of viewing people almost entirely based on their occupation- in other words the result of societies where work is the primary activity and closely interlinked with personality. In a libertarian communist society the hope is that there'd be much less need for 'work', and with it differing social status based on occupation - hopefully everyone would participate in both intellectual and manual (creative and executive) labour, or rather the division between them would be superceeded.
Authority: this means two things.
Institutional authority where someone's position in society gives them authority over others, almost always backed up by force.
And the authority of knowledge or experience - where someone is seen as an authority on a subject (theoretical physics, making shoes, heart surgery, house building). Sometimes the two kinds go together, often not.
Most anarchists don't have a problem with the second kind, as long as anyone with that knowledge isn't put in a position where they have control over other areas of life, or most importantly where they aren't accountable and recallable to the community.
Although I've not read the Rousseau you mentioned, it's very important to place ideas in their historical context, and Rousseau's context was that of defending certain social relationships (bourgeios ones) which were taking on the old hierarchies of feudalism and family lineage. As such his views shouldn't be viewed ahistorically but as the product of the times he lived in, and the purpose his views were supposed to serve.