But I do assume that the consciousness of other humans is rather like my own.
I assert that we can and do make this observation as a direct result of language. The language allows us to communicate, verbalize abstractions, evidence comprehension, coordinate, plan, organize, predict, love, etc.
Such language has not been observed in lower beings.
Do you assume that infants are not conscious? How about people born deaf prior to the invention of sign language?
If you believe these people are conscious, do you have any evidence other than non-verbal behavior and similarity of brain structure?