I see "egalitarianism" as "equality of opportunity". That, and "equality before the law".
But even with the same starting conditions/talent/upbringing/genes, some people will climb further than others. Effort, creativity, etc. We as society should encourage that and reward people who achieve more, for the common benefit of all.
After all, people with advantages rise to the top, whether that's upbringing, talent, or gene.