The word "phishing" can't be found in Chaucer or Shakespeare. It is a homophone of "fishing". But why "ph" instead of "f"? Many English words of Greek origin transliterate "φ" (phi) as "ph" (for example, φωτός (light) and γράφω (write) became photography in English).
The Latin alphabet, on the other hand, didn't have a letter φ and used "f" for the voiceless labiodental fricative sound. However, I don't think the origin of "phishing" lies with the ancient Greeks. One theory, which I haven't substantiated, is that "phishing" is the modern version of "phreaking" which described the practice of proto-hackers of obtaining free long distance phone calls from Ma Bell.
Lest there are any Classicists among the readers, it must be noted that the ancient Greeks did at one time use a form of "f" in their writing. This letter is known as digamma ("ϝ"). It occupied the sixth position in the alphabet and was later adopted by the Etruscans and then adopted into Latin as the sixth letter, "f". The Greeks, however, eventually dropped it.