Final answer:
Agamemnon refuses to walk on the tapestries out of respect for art.
Step-by-step explanation:
Agamemnon refuses to walk on the tapestries because of respect for art. In Greek culture, tapestries were considered valuable works of art and walking on them would be disrespectful. This is shown in the play 'Agamemnon' by Aeschylus, where Agamemnon refuses to step on the tapestries spread out for his entrance and instead insists on walking on a purple carpet.