This question already has an answer here:
Rashi at the beginning of Vayechi (Bereishis 47:28) asks:
לָמָּה פָּרָשָׁה זוֹ סְתוּמָה
Why is this Parsha “closed”?
As Sifsei Chachamim ad. loc. explains:
למה פרשה זו סתומה כו'. כלומר קבלה הוא בידינו מעזרא ע"ה שפרשת ויחי הוא תחלת פסקא ולא חדא פרשה היא עם וישב ישראל וכו' ודרך פרשה סתומה שיעורה ט' אותיות והכא כולה סתומה ואין בה ריוח כלל:
That is to say: There is a tradition in our hands from Ezra, peace be upon him, that Parshas Vayechi is the beginning of a passage, and it is not one parsha with “and Yisrael dwelled” [i.e. the end of Vayigash, whose final passuk begins with that]. The way of a closed parshah is [to have a gap] measuring 9 letters, but here it’s entirely closed, and there is no gap at all.
Is there a problem with beginning a Sidra in the middle of a Parsha, and that’s why the question is asked here? Or is there really no problem with beginning a Sidra in the middle of a Parsha, and the question is merely why the custom is that only at Vayechi do we do so? Or, a third option, even at Vayechi we don’t begin in the middle of a Parsha; Rashi’s wording of “Parsha” implies that the tradition is that this is a new Parsha, just like any other place where there actually is a gap.
Which understanding of the question is correct?