I think Dumbledore is (portrayed as) someone who _does_ strongly believe in roles, tropes, and categories, and who thinks death is a tragic, but necessary and inevitable part of life. He would think it absolutely permissible to set fire to a chicken (magical or normal) if there were some reason (including a reason as vague as “necessary to impress Harry that I’m mysterious”).
I think Dumbledore is (portrayed as) someone who _does_ strongly believe in roles, tropes, and categories, and who thinks death is a tragic, but necessary and inevitable part of life. He would think it absolutely permissible to set fire to a chicken (magical or normal) if there were some reason (including a reason as vague as “necessary to impress Harry that I’m mysterious”).
But Harry don’t believe in that, so he still was should ask if the chicken was completely normal except it was magical, not?