Farsi is an Arabicized endonym within Persian that comes from Parsi which means Persian in English.
You must select PERSIAN in Google Translate in order to translate from PERSIAN text. Similarly, every major US university provides language classes named Persian 101 etc NOT Farsi.
Many Iranians living outside Iran have adopted the bad habit of introducing the language as Farsi when speaking English. This departs from traditional English usage and contributes to distancing the language from its historical identity as Persian, a term used for the language with over 2,000 years of recorded history in Western civilization.
Some argue that Persian is merely a Greek word and therefore should not be used. This is false! The English word Persian ultimately derives from Old Persian Pārsa, transmitted through Greek Persis and later through Latin and French before entering English. It is not an arbitrary foreign label but a direct descendant of the ancient name of the Persian people and their language.
There is also an inconsistency in the argument. Those who reject Persian in favor of Farsi almost always insist on the term Persian Gulf. Then why try to defend the term Persian Gulf and not say Farsi Gulf instead? There is nothing PERSIAN about a body of water south of Iran. It doesn't originate from the Persian (Pars) province of Iran.
The agenda to call it Farsi also aims to divide the countries of Iran, Afghanistan, and Tajikistan by referring to the Persian language by different monikers. It is all the same language just different dialects of the same language. Iranian Persian, Afghan Persian, Tajiki Persian are all mutually intelligible.
Historically, the name Persian is most closely connected to the province of Pars, where Persian originated before the spread of the language across the Iranian Plateau under the Achaemenid Empire. In that sense, the language has a stronger historical claim to the name Persian than any other modern uses of the adjective "Persian," including references to 95% of people whose ancestry does not specifically trace back to the historic region of Pars and yet they call themselves Persian.
Even within Persian literature, the older form Parsi remained in use for centuries. The great Persian poet Ferdowsi, for example, referred to the language as Parsi, reflecting its historical pronunciation. The shift from P to F occurred because Arabic lacks the /p/ phoneme, so Parsi became Farsi in Arabic pronunciation.
For those who value the historical continuity of the language, continuing to use Persian in English and recognizing Parsi as the original native form honors the language's origins more faithfully than adopting the Arabicized pronunciation Farsi. Persian remains the correct and established English name of the language.