Boromir's ultimate, freaky motives...

[Boromir88]

I thought about that too Estelyn, but I think of it more to emphasize Boromir's pride about himself. He thought he was the best as did Faramir. I don't think that it means Boromir didn't feel confident in his brother. It just goes to emphasize Boromir's pride in himself. Boromir and Faramir had a brotherly bond, and eventhough if Boromir saw himself as unrivalled, I don't see why he would feel that his brother was incompetant.

why would the leaders of Gondor have chosen to send away the leader of their army?!

And that still remains the biggest question. Perhaps they felt like he was the best for the job? I mean they wouldn't suspect of any danger that may happen to Boromir. He's going to Rivendell to get some advice from Elrond, and returning, they wouldn't expect anything bad that may happen. But, what still is the hard thing to figure out is exactly what you said, why send the leader of your army if you are facing pressure from Sauron and having to fight him off?