Primogeniture in any form is discriminatory precisely since birth order is an immutable, permanent, unchosen characteristic assigned randomly at birth, just like race or sex.
The oldest child is the most likely to survive. It is a rational and fair rule in such context.
“Fair” is a much trickier beast! My favorite approach to conceptualizing fairness is Rawls’ veil of ignorance: if you were going to be placed as a random member of society, rather than your current position, and you would still support a policy given this change, then the policy is fair. Knowing that, beyond the veil of ignorance, I may be a paraplegic, would I still support dismantling the ADA’s wheelchair accessibility requirements?
When you have to struggle for life, discriminating against some categories, such as disabled people is necessary for the whole group to survive. Animals do it, and humans in antiquity did it too, out of necessity. It's actually how evolution happens. Humans still do it to some extent when they choose how to mate : they discriminate.