In one part of the Birkat Hamazon we say "veal hakol... anu modim lach umevarchim otach".
This is only one small example, and there are many others, but why is God being adressed in the feminine "lach" and "otach"?
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The Torah varies between the pronominal suffixes for second person masculine singular with sh'va before kamatz and the reverse, with the latter appearing more in pausal positions. Both are, as evidenced by the contexts in which they appear, masculine.
The variation (as opposed to one of the two appearing consistently) is visible in the line you quoted, as well as the next one, which is the pasuk it leads up to.
אֲנַחְנוּ מוֹדִים לָ
ךָבְּפִי כָּל חַי תָּמִיד לְעוֹלָם וָעֶד:
תָּאֶת ה' אֱלֹהֶי
ךָעַל הָאָרֶץ הַטֹּבָה אֲשֶׁר נָתַן לָ
That is, what may look like m. m. f. - all with the same referent, followed by what looks like m. m. m. m. f. - all with the same referent.
I am no genreist, but there are clues in birkas hamazon that it was written in the style of Biblical Hebrew. (An example is the use of the particle "נא".) So the pattern of this standard alternation between forms in Biblical Hebrew makes sense to appear in birkas hamazon as well.
I realize as I am writing this that the answer (and possibly the question) already appears here.
As noted here by Rabbi Elchanan Lewis, in response to the same question:
In biblical Hebrew the feminine Lach is used for the masculine form as well in hundreds of cases. (Gen. 3;18 4;6,12 14;21,23 15;1 just to mention a few)
See, however, the answers to this question, from which it seems that actually the suffix is the Mishnaic Hebrew version of the masculine.
That said, Rashi comments on Numbers 11:15:
ואם ככה את עושה לי. תָּשַׁשׁ כֹּחוֹ שֶׁל מֹשֶׁה כִּנְקֵבָה כְּשֶׁהֶרְאָהוּ הַקָּבָּ"ה הַפֻּרְעָנוּת שֶׁהוּא עָתִיד לְהָבִיא עֲלֵיהֶם עַל זֹאת, אָמַר לְפָנָיו, אִם כֵּן, הָרְגֵנִי תְּחִלָּה:
ואם ככה את עשה לי AND IF THOU DO THUS WITH ME [KILL ME, I PRAY THEE …] — The Hebrew word for “Thou” appears in the feminine form את instead of the masculine אתה to intimate that Moses’ strength grew weak as that of a woman when the Holy one, blessed be He, showed him the punishment which He was to bring in future upon them for this (for their sin). He, (Moses) therefore, said before Him, “If so, kill me first” (Sifrei Bamidbar 91).
The Maharal (after rejecting other interpretations of the passage) seems to explain there that Moshe's perspective of the Divine influence was weakened as a result of his frustration with the nation's baser tendencies. Accordingly, Moshe did not witness the Divine influence in his usual way of gevuroth hashem - the might of G-d, associated with the miraculous/subjugation of the natural order. The "might-of-G-d" perspective is that encapsulated by the masculine pronoun; whereas this diminished, weaker perspective is associated with the feminine pronoun. (Notably, actually ascribing weakness to the Divine is heresy in the eyes of Judaism. These explanations are focused on the diminished ability of the person witnessing divine influence.)
Likewise, one might explain that the usage of feminine-seeming forms in our liturgy, might also, on a deeper level, reflect our inability in this world of exile and suffering, to experience the divine at the masculine level of gevuroth hashem. So instead, we thank Him from our diminished perspective of His "natural" influence.
(See also Berakhoth 32a.)
This is an interesting question and hopefully, the following answer will offer some insight and something to reflect upon.
The G-d we pray to is one, above, meaning transcendent of all division including gender. That concept refers to G-d at the level of essence which is actually above names altogether.
In the first paragraph of Birkat HaMazone, that level is referenced by the statement:
הוא-נותן לחם לכל-בשר
This is similar to the language in the Kedushah for Musaf of Shabbat after saying the first line of Shema. It means that G-d, at His essence (referred to without any name but simply as He in this case) is the actual Giver and Provider of everything.
Then slightly further in the first paragraph is introduced the first concept of one of G-d's names, Havayeh (יהוה). This name is masculine (even paralleling the physical form of a human male, head, shoulders and arms, torso, and hips and legs) and also associated with the first man, Adam (אדם), who is similar to G-d's name Havayah (דומה לעליון). This follows the teaching of Rabbi Menachem Azaryeh of Fano in his explanation of Bereshit 2:20 (ולאדם) from his discourse, Em Kol Chai regarding the cantillation note, Zakef Gadol above it which has a gematria value of 26 like this particular name of G-d.
The second paragraph to Birkat HaMazone then changes, as you have noted, to feminine when referring to G-d. This name of G-d is addressing (אהיה) which also relates to the feminine. This connection is somewhat more complicated.
These names of G-d also have what are called expansions of those plain names. They are often referred to by their numerical values. One of the expansions for Ehyeh is 161 which is written (אל״ף, ה״י, יו״ד, ה״י). And this expansion is equated with the name that is actually mentioned in the opening lines of Bereshit dealing with the creation and formation of the first man and woman. That name of G-d associated with the first woman is Tzelem (צלם) which actually parallels the physical form of the human female. And that name, including the kollel for the whole name itself is also 161 just like the expansion of Ehyeh.
So in terms of intention, the gender switch in the second paragraph of Birkat HaMazone is referring to this name of G-d.
And in this context, it is worth pointing out that these two, four-letter names of G-d (אהיה-יהוה) which correspond to the concepts masculine and feminine, meaning husband and wife, originate from the one, single, six-letter name of G-d, (אהיהוה) which alludes to the union of husband and wife. This was the original state of man, meaning male and female were actually created as one, single being.
And the creation of the first man (אדם הראשון) also parallels the creation of light (a single light with no source) on the first day and then the creation of the two great (and initially equal) sources of light on the fourth day. This single, six letter name of G-d is actually alluded to in the first posuk of the Torah.