One terutz, in a nutshell [poor terutz - stuck in a small nutshell....]: Even according to the opinions that allow one to fast on Rosh Hashana, it is ALSO a mitzvah to eat. Meaning, that if one fasts according to all of the details of the laws of fasts i.e. he accepted upon himself the fast in advance, then the fast OVERRRIDES the mitzvah to eat. This is because fasting is an act of teshuva. But if one does NOT accept the fast in advance, and just ends up not eating until chatzos because there was no food around, he must now go ahead and eat and may not finish the day with a fast. The MITZVA require a קבלת תענית in advance while the איסור to fast does not.
So it emerges that according to EVERYBODY there is a mitzvah to eat on Rosh Hashana as the pasuk in Nechmiah says "אכלו משמנים ושתו ממתקים". Just according to some, the value of a fast of teshuva overrides that mitzvah under certain circumstances. But the mitzvah to eat [and איסור to fast] never went away.
[עפ"י דברי הפחד יצחק ראש השנה מאמר כ"ב]
So now we can understand the gemara's question לכולי עלמא: Why do we need the third of Tishrei in Megillas Taanis to forbid fasting on the second - one should be forbidden because it follows the first of Tishrei which in principal is a day that one is forbidden to fast!!
