Why is the volitional form being used here?
荒地{あれち}の魔女{まじょ}に張{は}りあおうなんて いい度胸{どきょう}ね (Source: Howl's Moving Castle)
Is it that なんて is functioning as a kind of quotation particle here as well as its more usual part as a nominaliser?
I say that because Maggie Sensei wrote something quite far down in her article on using なんて that it can operate in this role as well sometimes. I've not come across any other sources referring to this, though.
So effectively, in as direct a translation as I can muster, what is being said is: "to say that you will compete with the witch of the wastelands - you have some nerve!"