First, the article needs an ending in -ν. Σαν την άλλη. Remember never to omit it.
Second, σαν (a contraction of ωσάν) ushers comparisons and similes and is followed by an accusative. Σαν τον αϊτό είχα φτερά ...
Third, the speaker, a man, takes the woman's statement too literally, and thinks...