I suspect that Boromir could have requested a low-key introduction. I think it’s likely that he would actually be very embarrassed to have to come to Rivendell for help. We know how Gondor-proud he is, and we know that Gondor is in terrible danger at the moment and might fall to Mordor soon. They’re losing ground, people are dying, and they’re getting desperate. So what’s their big move? Boromir, next in line to be steward of Gondor, has traveled away for 110 days to look for a house that no one knows how to find to talk to a wise elf about a funny dream he had. That has to feel pretty humbling, right? I suspect he’d much rather be at the front lines than hunting for a lost elf house. (It’s Faramir who thinks that kind of thing is important). To top it off, when he gets there, rather than having a private chat with Elrond he has to attend this council to hear the answers to his question. And of course, the council is attended by assorted princes, wizards, elf lords, and other extremely important people so he has to admit in front of everyone that Gondor's big hope at the moment is that the meaning of a dream-poem is super important (it is super important, but that probably feels really unlikely to him). I’m sure there’s a part of him that would like to downplay how utterly desperate Gondor must be to send him on this mission. (The other part of him apparently wins out, since he does mention that Denethor, Lord of Gondor, is his father but it does take him a little bit to get there).
I also think that he would consider coming on this mission be taking one for the team. It suggests he has faith in his brother to handle the war front while he’s gone. He says in the council that Faramir was eager to come but, “since the way was full of doubt and danger, I took the journey upon myself.” Faramir says something similar when he meets Frodo and Sam. Faramir took him at his word, but I don’t. I bet Boromir thought that he was being the bigger man. He was leaving the place that he thought was the most important place in the world that’s currently in danger of invasion, and he’s leaving his brother to be in charge of defense so that he can do a mission for him (Faramir) that Boromir probably considers very foolish. Boromir probably doesn't have any practice at acting humble, though, so he doesn't strike quite the right tone.
I've never known quite what to make of the fact that Boromir comes on this journey instead of Faramir when all available evidence suggests that Faramir should have come. It doesn't make sense to me that Boromir would think Faramir wasn't up to the journey if he's willing to leave the defense of Gondor in his hands. It also doesn't make sense to me to say that Boromir wanted the honor of coming to Rivendell himself because we'll find out later that it's Faramir who would be excited about that kind of thing. I'm not sure "trying to do the right thing and sort of messing it up" is a totally satisfactory explanation, so I'd love to hear your thoughts!
I also think that he would consider coming on this mission be taking one for the team. It suggests he has faith in his brother to handle the war front while he’s gone. He says in the council that Faramir was eager to come but, “since the way was full of doubt and danger, I took the journey upon myself.” Faramir says something similar when he meets Frodo and Sam. Faramir took him at his word, but I don’t. I bet Boromir thought that he was being the bigger man. He was leaving the place that he thought was the most important place in the world that’s currently in danger of invasion, and he’s leaving his brother to be in charge of defense so that he can do a mission for him (Faramir) that Boromir probably considers very foolish. Boromir probably doesn't have any practice at acting humble, though, so he doesn't strike quite the right tone.
I've never known quite what to make of the fact that Boromir comes on this journey instead of Faramir when all available evidence suggests that Faramir should have come. It doesn't make sense to me that Boromir would think Faramir wasn't up to the journey if he's willing to leave the defense of Gondor in his hands. It also doesn't make sense to me to say that Boromir wanted the honor of coming to Rivendell himself because we'll find out later that it's Faramir who would be excited about that kind of thing. I'm not sure "trying to do the right thing and sort of messing it up" is a totally satisfactory explanation, so I'd love to hear your thoughts!