It's possible that Sterling Archer's rule about not having dogs in his apartment is due to his mother's love of Duchess. This is contradicted however by his revelation that he does in fact love dogs during a mission in Morocco ("Un Chien Tangerine"), although he quickly adds he hated Duchess for various reason one of which is of him cleaning the chimney while his mother celebrates the dogs birthday



Duchess may have held a hostile attitude towards Sterling as well, implied by her growling at him as a child when he sighed at his mother's overaffectionate actions towards her while cleaning the chimney.