Pepper's full name is Pippin Galadriel Moonchild, suggesting hippie parentage. She has a decidedly peppery temper and savagely bit the first child to mock her name at school. She would also be happy to tussle with her fellow Them, but the boys are becoming aware of the approach of puberty and so feel that "Laying hands on good old Pep moved things into blood-pumping areas that they weren't comfortable with just yet". Anyway, nice boys don't fight girls, just ask Banjo Lilywhite.
In the final showdown, it is somehow entirely fitting that Pepper should be the one who is tasked with facing down and temporarily destroying War. If the Four Riders of the Apocalypse are anthropomorphic personifications, the condensed essence of thousands of years of human hopes, dreams, fears, nightmares and general experience, then it makes sense that Adam's three closest chums should each have something of the essence of one of the Riders about them - and, being human, come out fully triumphant in the confrontation. Death is perfectly aware of this, which is why He concedes a draw with Adam.