Whats the reasoning behind יין פגום?

Question

There is an halacha called יין פגום (mentioned in Pesachim 106a and Shulchan Aruch Orach Chaim Siman 182) where if I drank a cup of wine for Kiddush or Birkat Hamazon and didn't finish all of it, I must either wash the cup or add more wine or a bit of water into it so I can drink from it again (I'm assuming for Kidush or Birkat Hamazon).

I have two questions:

1. Why does the cup become pagum? Should it not have the status of שארית מצוה (left overs of a mitzvah) which is a praise worthy thing to drink from?

2. Why just by adding water or more wine does it not make it not pagum any more?

Answer 1

Why just by adding water or more wine does it not make it not pagum any more?

Here's a kabbalistic view on why to add water to the wine (fun fact: in Dutch, we have a proverb called "water bij de wijn - putting water into wine" - taking compromises).

The Zohar says in parashas Shmini that wine represents gevurah and that (shining) water is on the side of chessed:

אֶלָּא שֵׁירוּתָא דְּחַמְרָא חֶדְוָותָא. סוֹפֵיהּ עֲצִיבוּ. וְעוֹד דְּיַּיִן מִסִּטְרָא דְּלֵיוָאֵי אָתֵי, מֵאֲתַר דְּחַמְרָא שָׁרֵי, דְּהָא אוֹרַיְיתָא וְחַמְרָא דְּאוֹרַיְיתָא, מִסִּטְרָא דִּגְבוּרָה הוּא. (ס"א סיפיה עציבו, וכהנא שירותא וסיומא בעי חדותא ונהירו דאנפין, יין אתי מסטרא דליואי) וְסִטְרָא דְּכַהֲנָא מַיִין צְלִילִין נְהִירִין. for the Torah and her wine are of the side of Gvurah, and the side of the priests is that of clear shining water, WHICH IS CHESED. (translation taken from here)

I saw an quote from the Ta’amei Haminhagim (not sure where, if anyone could add this in...) in saying that when you add water to the wine that is pagum, it will become "ready to drink again". This is because when you add chessed to gevurah, it will give you berachos, blessings.

See also the Tosfos ד"ה טעמו פגמו, where the Yerushalmi is quoted. The Tosfos says:

And he puts some water into the cup, so that it will appear to be unblemished. As it is stated in Yerushalmee: R” Yonoh tasted the cup and he corrected it by adding water or wine and the explanation is that after he drank from it he added a drop of water or wine to correct it and then he would recite havdoloh or kidush upon it. (emphasis mine)

Tosfos says that this way, it will appear to be unblemished.

Answer 2

Interesting question! Perhaps to answer your first question we'll apply the Gemara in Nedarim 49b (from sefaria),

רַבִּי יוֹסֵי וְרַבִּי יְהוּדָה, חַד אָכֵיל דַּיְיסָא בְּאֶצְבְּעָתֵיהּ וְחַד אָכֵיל בְּהוּצָא. אֲמַר לֵיהּ דְּאָכֵיל בְּהוּצָא לִדְאָכֵיל בְּאֶצְבְּעָתֵיהּ: עַד מָתַי אַתָּה מַאֲכִילֵנִי צוֹאָתְךָ, אֲמַר לֵיהּ דְּאָכֵיל בְּאֶצְבְּעָתֵיהּ לִדְאָכֵיל בְּהוּצָא: עַד מָתַי אַתָּה מַאֲכִילֵנִי רוּקְּךָ

Rabbi Yosei and Rabbi Yehuda dined together. One of them ate porridge with his fingers, and the other one ate with a fork [hutza]. The one who was eating with a fork said to the one who was eating with his fingers: For how long will you keep feeding me your filth? Must I keep eating off of your dirty fingernails? The one who was eating with his fingers said to the one who was eating with a fork: For how long will you keep feeding me your spittle, as you eat with a fork which you then put back in the common bowl.

Sipping from a cup automatically deposits some amount of saliva into the beverage, and the Passuk says הקריבהו נא לפחתך, something that's inappropriate for a human to consume don't use it for holy things either (I know that it's different when it's your own saliva, but perhaps it's still lacking the appropriate כבוד שמים), therefore we consider it Pagum.