Green’s Dictionary of Slang

wombat n.2

[pun on he ‘eats roots and leaves’/eats, root v. (5a) and leaves]

an unappreciative male.

jamesbrown Urban Dict. 🌐 Wombat 1. Wombat, eats, roots, shoots and leaves. [...] They call my mate the wombat, he goes home with a girl, eats, roots, shoots and leaves!