I think your starting premise is false. Egalitarianism doesn't mean that eveyone should have exactly the same opportunities in the sense of havnig the same chance to acquire a certain job/resource/luxury item/etc.

Egalitarianism means that there must not be any ARBITRARY limit imposed on one' access to any given opportunity.

What would be an arbitrary limit? Well, things like race, gender, sexual orientation, socioeconomic status, or other traits that have no necessary logical connection to a given opportunity, cannot be used to deny people equal access to those opportunities.

On the other hand, there will always be jobs for which things like intelligence, physical fitness, good looks, or other traits will be relevant to optimal performance. There's nothing wrong with that.

But more broadly, the concept of egalitarianism is rooted in the idea that every human life has equal dignity. Not that every life has equal worth in the sense that an actuarial table might calculate, but equal MORAL worth. And we take that stance because not doing so leads to dangerous outcomes like war, genocide, forced sterilization, mass incarceration, and other human rights violations.