Perhaps this situation has happened but it is not mentioned really in the Lord of the Rings universe. So perhaps it was just not recorded for one reason or another. In any case, all the famous elf-human pairings seem to be elven women marrying mortal men. And that's interesting. Surely at some point, an elven man must have fallen for a mortal woman. Or maybe not?
To understand the answer to these questions, it is crucial to understand the reasons behind the rare elf-human pairings.
For example, Aragorn and Arwen are the most well-known elf-human pairing in Lord of the Rings. Not only does Arwen choose to be mortal due to her love of Aragorn, she also plays a role in restarting the line of Kings of Gondor and Arnor. Though Arwen would technically be mortal at that point, she might still have the wisdom and strength of an elf. And that would be a good thing for the royal line to have. Therefore, Aragorn and Arwen's marriage serves a greater purpose in the story of Lord of the Rings.
These elf-human pairings are, therefore, not only love matches but also serve a purpose within the Lord of the Rings universe. For example, Beren and Lúthien manage to recover one of the Silmarils and therefore are important characters in the Lord of the Rings world. Beren actually passes on at one point but due to his love for Lúthien, waits for her in the halls of Mandos. She then manages to convince Mandos with a song to reunite her with Beren. Mandos, however, does not have the authority to do so, so he asks Manwë, who then asks Eru Ilúvatar. Lúthien is given a choice: she can either live with the Valar forever or she could live in Middle Earth again with Beren, but she would be mortal. Lúthien chooses the latter.
Arwen is actually a descendant of Lúthien, and is often compared to her. Like Lúthien, she falls in love with a mortal man, Aragorn. Both women are also extremely beautiful, considered the most beautiful of their times. Lúthien's granddaughter Elwing is actually the great-grandmother of Elrond and Elros. Elrond and Elros both get a choice whether they want to be counted among elves or men. Elrond chooses the elves, while Elros chooses men and becomes the first King of Númenor. Arwen and Aragorn's marriage also reunites the two lines of Lúthien's descendants. Therefore it serves that purpose as well as providing a parallel to the Beren and Lúthien relationship.
So why doesn't the reverse happen? Why are there no marriages between elven men and mortal women? Well, there could be several reasons for this. One possible reason is that elven men might have been a bit pickier than elven women when it comes to romantic partners. They would not have seen it as an attractive option to marry a mortal woman, even if they did fall in love with one, since for them elven women would always be better. Elven women, on the other hand, would be more open-minded and willing to risk it all to be with their mortal loves.
Another possible reason is that Lord of the Rings is a fantasy tale. Fantasy stories are full of unlikely couples, no matter how unrealistic they might sometimes seem to modern audiences. In addition, a story where a man from humble origins is revealed to be a prince or a king and marries a noblewoman is very common in the fantasy genre. The reverse is common as well, but perhaps not so much when Tolkien was writing Lord of the Rings. And even if it was, Tolkien might not have seen it as as romantic as the opposite. Especially since he somewhat saw himself in characters such as Beren, and viewed his wife as Lúthien to a certain extent.
And finally, another possible reason is that elf-human pairings are still rare in the Lord of the Rings universe. It could just be a coincidence that all the elf-human couples that are written about feature an elven woman marrying a mortal man. Also, apparently, there was a case where an elven man, Aegnor, fell in love with a mortal woman, Andreth. However, at the time the elves were at war and they did not want to get married or have children during wartime. Aegnor later ends up passing on, and Andreth is left grieving.
Perhaps that is another reason that elf-human pairings are so rare. Unless there is some intervention from Eru Ilúvatar or some other divine force, elves and humans have very different fates. And it would be tragic to be separated from the one you love forever. So Tolkien instead opts to have the few elf-human couples have a slightly happier fate.