Our Gemara on amud aleph discusses one of the most unusual executive powers accorded to the Rabbis of the Sanhedrin to enforce certain critical social norms and functioning. There are times where they are able to annul a marriage that would technically still be binding according to strict Torah law (though poskim debate the lomdus of the exact halakhic mechanism). In order to allow for the smooth functioning of society, certain overrides were put into the law by the rabbis. For example, somebody who sends a messenger to deliver a divorce bill but then changes his mind. Technically, he should be able to verbally revoke it (just as in secular law, one can revoke power of attorney verbally, even if it is in writing). Yet, one can see how much chaos that could cause if somewhere across the sea, the messenger is delivering the Get, and on this side of the ocean, the husband has annulled the agent's status. This is why the rabbis maintained that the marriage is dissolved, even though technically, the divorce was invalidated by the husband.
וּמִי אִיכָּא מִידֵּי דְּמִדְּאוֹרָיְיתָא בָּטֵל גִּיטָּא וּמִשּׁוּם מָה כֹּחַ בֵּית דִּין יָפֶה שָׁרֵינַן אֵשֶׁת אִישׁ לְעָלְמָא אִין כׇּל דִּמְקַדֵּשׁ אַדַּעְתָּא דְּרַבָּנַן מְקַדֵּשׁ וְאַפְקְעִינְהוּ רַבָּנַן לְקִידּוּשִׁין מִינֵּיהּ
The Gemara asks: And is there anything that by Torah law renders the bill of divorce void and the wife remains married, and due to the reasoning of: What advantage does the court have, we do not recognize that the bill of divorce is void and permit a married woman to marry anyone? The Gemara answers: Yes, anyone who betroths a woman betroths her contingent upon the will of the Sages, and when one fails to conform to their will in matters of marriage and divorce, the Sages expropriated his betrothal from him retroactively.
Rav Naftoli Yaakov Hacohen (1884-1971, Sefer Savar Naftali, Shemini, page 40) offers a delightful derash to give more insight into Nadav and Avihu's sin and demise (the Sons of Aharon who brought the "strange fire" and died for it (Vayikra 10:1-2).
The mitzvah to have children, and by association to marry, can be considered as if one is behaving as God's agent. Because, after all, God is the Creator. When humans have children, they are fulfilling His will to create. One of the sins that the Midrash Rabbah says that Aaron's sons committed, which led to their death, was that they did not marry, it would seem from a certain arrogance, as in no woman was good enough for them (Vayikra Rabba 20:9-10). This can be understood then as a failure to follow out God's agency to create more children in the world. If so, this gives us a deeper understanding of why their offering was refused. First of all, by bringing an extra fire, they must've imagined, somehow, that they were inspired to fulfill God's will that they intuited. Furthermore, we know that the Cohanim can be referred to as שלוחי דרחמנא or "God's agents" (Kiddushin 23b). Therefore, since they had failed to fulfill God's primary directive and agency, their enhanced efforts to fulfill God's agency by offering a voluntary additional fire were met with rejection and catastrophe.
Rav Naftali Yaakov adds that this is why it is a special mitzvah on Yom Kippur for the Cohen Gadol to be married (Yoma 2a). If he is married, it shows he is devoted to being God's agent and fulfilling His will in this world by being a creator of more children. Therefore, it puts him in a good place to serve as God's messenger, especially on this most intense and holy service of the year.
And now, for the pièce de résistance: This is how we can understand the mechanism by which the Sages were able to annul and uproot the marriage. Since we saw that marriage is any way acting as an agent of God and fulfilling His shelichus, we might also say that since he marries under the guidance of the Sages, the Sages are God’s agents that allow him (the husband) to perform God's agency through the Sages’ agency. Since the assignment of agency is expressed verbally, it is one of the easiest matters to annul and cancel. Therefore, the Sages were able to uproot the marriage because they were able to invalidate the original agency (marriage as an agent of God's directive).
But I will go one step further than Rav Naftali Yaakov went, and I even wonder why he didn't say this explicitly. There is strong poetic justice to this Rabbinic enactment. The husband is unfairly revoking his authorization of the agent to give his wife the Get. Therefore, it makes sense that the rabbis would counter with, "You want to revoke your agency and therefore stop the divorce. We will counter you on your own terms. We will revoke our authorization for your agency, which invalidates your marriage from the very beginning. You were supposed to carry out God's will as His agent, and we are now retroactively stripping you of those powers, and so your marriage dissolves."
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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