Our Gemara on Amud aleph discusses contradictory verses regarding where the Cherubs on the Holy Ark faced, acting as a bellwether of God’s pleasure or disappointment with the Jewish nation:
How were the cherubs standing? Rabbi Yoḥanan and Rabbi Elazar disagree about this. One says: Their faces were turned one toward the other. And one says: Their faces were turned toward the House, i.e., the Sanctuary. The Gemara asks: But according to the one who says that their faces were turned one toward the other, isn’t it written: “And their faces were toward the House” (II Chronicles 3:13)? How does he explain the meaning of this verse? The Gemara answers: This is not difficult, as their faces miraculously changed directions in reflection of the Jewish people’s relationship to God. Here, when it states that the cherubs faced each other, it was when the Jewish people do the will of God. There, the verse that describes that the cherubs faced the Sanctuary and not toward each other, was when the Jewish people do not do the will of God.
The Ritva (Yoma 54b) famously asks: The Gemara (ibid) teaches that when the gentiles captured the Temple Mount and invaded the Holy of Holies, they saw the naked Cherubs in an intimate embrace, and mocked the Jews for having this seemingly obscene artifact in the holiest of places. But if the Cherubs turn away from each other when God is displeased, which surely must have been the case during the destruction of the Temple, why were they in an embrace?
The Ritva gives a simple explanation. At that moment, God’s anger was expressed by the humiliation of the Jewish people being debased, so the Cherubs assumed a position that manifested that reality. Peri Tzadik, (Rosh Chodesh Adar 5:1) offers a deeper psychological explanation. The Jews were in denial that God would really punish them and that they would be militarily defeated, therefore they did not repent. However, the moment the Gentiles invaded and the Jews saw it was for real, they then began to repent. Therefore God was pleased at that moment, despite repentance no longer adequate to reverse the divine decree.
Another explanation that occurs to me is that it mirrors the archetype of a divorcing couple, who after the decision was made to end the marriage and there was nothing left to fight over, ironically may have a moment of nostalgic closeness. So too, God’s compassion and love was aroused at the darkest of times.
A final thought to answer this contradiction is that since the ability of the Cherubs to be animated was clearly a miracle, perhaps it was a vision. If so, the viewer might really be seeing themselves reflected in the position of the Cherubs. If a Jew looked at them, he saw God’s dissatisfaction. If a Gentile looked at them, he saw something indecent because of his own lewd nature. The ultimate message may be that when we see flaws in others, this may be a reflection of our own deficiencies.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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