In the Bedtime Shema, (Artscroll Sefard Edition), the opening verse says: "I hereby forgive anyone..." but ends with "I forgive every Jew."
Why does it not say "... and every Gentile?" Ultimately, all come from HaShem and all require forgiveness. Why not carry through the universality?
The pre bedtime prayer states: Master of the Universe, I hereby forgive anyone who angered or antagonized me or has sinned against me. It continues: No person (Hebrew = adam) should be punished because of me.
You ask about the words "I forgive every Jew". This is a translation from the Hebrew words lechol bar Yisrael, literally meaning "to all sons of Israel". These words are found in some prayer books such as the Art Scroll (both Ashkenazi and Sephardi) and first appeared in print in 1662. However, an alternate reading is lechol ben adam, literally meaning "to all persons". This is the version used in two other popular prayer books, the Koren Siddur and Rinat Yisrael. The second version may well have been the actual original phrase as it flows better in context. A similar prayer can be found in Tefilla Zaka recited in the beginning of Yom HaKippur (Day of Atonement services) where the term indeed is lechol adam, to all people.
The Talmudic source for the idea of forgiving other people at bedtime can be found in tractate Megillah 28a where Rabbi Nehunya ben HaKanah, a 1st-2nd century Mishnaic sage, is asked how he merited a long life. In his response he notes that he never went to sleep with a curse against a friend. The Talmud exemplifies this with a description of Mar Zutra's practice of exclaiming before he went to sleep: "I forgive all who have caused me sorrow".
The pre-bedtime prayer that you quote is attributed to the Ari, Rabbi Isaac Luria in Safed in the 16th century who instituted a series of tikunim, meditative type inner rectifications that affect one's personal life on both the emotional and spiritual levels of existence. Before going to sleep one should first feel forgiveness towards others and then it is possible to turn towards God to ask forgiveness for oneself. Once one is in the forgiving mode of feeling, then it is appropriate to ask God for unconditional forgiveness. Therefore, his prayer concludes: "May it be Your Will, Hashem (God)… that you wipe away my sin with Your Infinite Mercy…". This idea of the Ari might be based on the verse in Isaiah 43:25, where God proclaims forgiveness to Israel for their sins without any prerequisite condition. Not even penitence is mentioned. God forgives simply for "My Own Sake".
Safed kabbalists in the time of the Ari had some rather universalistic expressions of compassion and love for all. Rabbi Hayyim Vital, Shaarei Kedusha, I: 5 states we should love all people, regardless of religion. Rabbi Moshe Cordevero, Tomer Devorah, requires having compassion for all people, indeed for all sentient beings. This is part of a religious-ethical imperative that is called imitatio Dei.
It seems therefore, that the original pre bedtime prayer of the Ari was meant to stimulate a mode of all-inclusive forgiveness. In the more insular societies where interaction is within a closed Jewish community this would mean forgiving fellow Jews. In the open pluralistic environments it can be rendered in its all-inclusive version of forgiving everyone.
 The source is Rabbi Natan Neta Hannover's siddur, Shaarei Tzion, Prague, 1662, under Tikun Keriyat Shemah, gate 5. This is a collection of mystical prayers and religious customs taken mainly from Kabbalistic sources. Rabbi Hannover died in Moravia in 1663.
 This can be found for example in the sidur of the Hida, Rabbi Haim Yosef David Azulai (1724 – 1806).
 Mar Zutra was a sixth generation amora, Talmudic sage in the early 5th century who headed the Yeshiva of Pumbedita in Babylonia.
That you have carefully read the words of the recital of Shema Before Retiring for the Night is impressive. A few words of explanation are required before answering your specific question. While some Talmudic sages sanction the recital of the Shema before sleep, others dispute the need. Rabbi Nahman, for example, exempts scholars from the recital (Berakhot 4b) since their constant engagement in study makes the need for any further Scriptural recitation unnecessary. In the Middle Ages, many rabbis saw the bed-time Shema as a means of protection against demonic forces. Moderns, who largely reject the very idea of demonic forces - let alone the efficaciousness of the Shema in warding them off - might still find the Zohar a suitable justification for the practice. The Zohar (Balak 211; Terumah 141) teaches that it is a noble idea to praise God before retiring.
Once the rationale for the universal practice of reciting the Shema before retiring was established, additional prayers were appended to the Shema itself, including a prayer for forgiveness. The Sefardic version of Rinat Yisrael (the “official” Israeli prayer book) includes an introductory prayer for forgiveness from all, that is, no differentiation between Jews and non-Jews. Unlike the Artscroll Siddur, there is no concluding prayer for forgiveness from Jews alone. Your question, therefore, is not directed towards the text of the Sefardic siddur but to the editors of Artscroll. It would seem that the latter have not resolved the conflict between universalism and particularism in Jewish prayer. Consequently, Artscroll features prayers of both type within the same service. You, however, may confidently include only the universalistic version, a version that comports with the opinion of Israel’s Chief Rabbinate.
The form of the prayer that you cite is not regularly found in other prayerbooks. I looked at several standard orthodox siddurim – Rinat Israel, the Hertz prayerbook, Siddur Metzudat Avraham, among others – none of them include the phrase you mention. It does seem to be included in Sefardi prayerbooks and those of the Chabad movement, as well as Artscroll. I know of no non-orthodox prayerbook that uses the text you cite.
For a fuller explanation on the origin of the prayer and that particular text I would refer to the response given by Rabbi Natan Ophir to your question. Here are some additional thoughts.
Israel Abrahams, in his A Companion to the Daily Prayerbook, pg 213, sets the ideal scene for the prayer:
This duty [to recite the bedtime shema] responds to a deep psychological truth. The text on which the Talmud founds the duty is Psalm 4:4 “Stand in awe and sin not: commune with your heart upon your bed, and be still.” To fill one's mind with high and noble thoughts is a wise preparation for the hours of silent night. The presence of the pure excludes the impure, and the meditation over the good drives drives out the suggestions of evil. Let not my thoughts trouble me, nor evil dreams, nor evil fantasies – so runs the phrase in the night prayer, and man takes the best means to ensure a rest perfect before God by ending the day with thoughts of God.
The goal of the prayer is to place oneself before God in the most blameless way possible – and that includes going to sleep with no malice toward any person – regardless of their background.
The Kitzur Shulchan Arukh [Chapter 70: The Maariv (Evening) Service, paragraph 3] underscores that ethic.
It is proper for every God-fearing man to examine his deeds of the past day, before going to sleep. If he finds that he has transgressed in any way, he should repent, confess and wholeheartedly resolve not to repeat the transgression..... He should also resolve to forgive anyone who has wronged him, so that no man may be punished because of him; for the Talmud says (B. Shabbat 149b): “He on whose account a fellow man suffers punishment is not admitted into the presence of the Holy One, blessed be He.” He should say three times: “I forgive anyone who has annoyed me,” and then say, “Creator of the Universe, I forgive,” etc.
Here we also see that the focus is on the way one places themselves before God in the most blameless way possible. By forgiving all people one opens the way to dwell in the Divine Presence.
I have no information about when or why the phrase, “I forgive every Jew,” was added. It seems unnecessary; after all, once you forgive every person at the beginning of the prayer you have automatically included every Jew. It also seems to be somewhat at odds with the ethic which informs the prayer – that which is described in the two quotes noted above. Given a choice I would choose to pray with what seems to be the most standard text, the one that excludes the restrictive phrase you cite.
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