I thing about it like this now - the fighting is mainly due to status/hierarchy. The older one needs to establish (and secure, secure, secure...) his/her postion as first born. The younger one loves to challenge that. Seems so archaic, bit isnt this how we are wired psychologically?

I guess as a father I would start to think hard, if I noticed that the older one would pick fights constantly that are utterly unprovoked (and, dont be fooled, those younger ones are usually experts in challenging their older siblings in VERY subtle ways!).