It is fascinating that we find an incredible likeness in the Beis HaMikdash between the relationship of HKB”H with the congregation of Yisrael and the relationship between a husband and wife. Let us refer to the Gemara (Sotah 17a): "דריש רבי עקיבא, איש ואשה זכו שכינה ביניהן, לא זכו אש אוכלתן"—Rabbi Akiva expounded: If a husband and wife are meritorious, the Shechinah is present between them; if they are not meritorious, they are consumed by fire.
Rashi provides the following clarification: "שכינה ביניהן, שהרי חלק את שמו ושיכנו ביניהן, יו"ד באיש וה"י באשה. לא זכו אש אוכלתן, שהקב"ה מסלק שמו מביניהן ונמצאו אש ואש." The letters י"ה from G-d’s name are split between the man and the woman; the letter “yud” appears in the word אי"ש, while the letter “hei” appears in the word אש"ה. If they are not deserving, HKB”H removes His name from them; as a consequence, they are consumed by fire, because all that remains is א״ש and א״ש --two opposing, conflicting, devastating fires.
We learn from Rabbi Akiva that the name י"ה alludes to the holy Shechinah—the divine presence. In fact, the Megaleh Amukos (Vayeira) writes that the word שכינ"ה can be broken down to "שכן י"ה"—indicating that the name י"ה dwells among the people of Yisrael. This is also brought down by the Shela hakadosh.
The dwelling of the Shechinah between a husband and wife via the name י"ה was mirrored in the Beis HaMikdash—the special place where HKB”H secluded Himself and united with the people of Yisrael. This is the implication of the passuk: "ועשו לי מקדש ושכנתי בתוכם"—and truly reflects Rabbi Akiva’s pronouncement that if a husband and wife are meritorious, the Shechinah is present between them. Now, we learn in the Mishnah (Midos 2, 5) : "וחמש עשרה מעלות עולות מתוכה לעזרת ישראל, כנגד חמש עשרה מעלות שבתהלים, שעליהן הלויים אומרים בשיר". There were fifteen steps going up from the “Ezras nashim”—the women’s courtyard—to the “Ezras Yisrael”—the men’s courtyard; they corresponded to the fifteen songs of ascension—Shir HaMa’alos—in sefer Tehillim; and the leviim would stand on them and sing. The Kli Yakar (Vayeira) explains that those fifteen steps in the Beis HaMikdash represented the name י"ה, which has a numerical value of fifteen. Thus, they signify the presence of HKB”H among the people of Yisrael like His presence between a husband and his wife.
With this in mind, we can begin to comprehend why HKB”H burned down the two Batei Mikdash with fire when Yisrael sinned. Referring back to the pronouncement of Rabbi Akiva, he said emphatically: “If they are not meritorious, they are consumed by fire.” Since HKB”H removes the name י"ה from them, all that remains is a consuming, double-dose of fire— אש אש. As the passuk says (Tehillim 74, 7): "שילחו באש מקדשך"—they have sent up Your Sanctuary in flames. This is what happened to the two Batei Mikdash. When Yisrael were no longer meritorious, HKB”H removed His Shechinah and the name י"ה from them, and they were consumed by the remaining, intense, double אש אש.
