Awesome gambit by Birdway with her flintlock right there and even more awesome counter-speech by Touma.
As others have said some are missinterpreting what Touma said. He's not saying Birdway is evil or completely in the wrong, he's saying than there was an option of using him as bait with rumors that may have worked and would have prevented thousands of people in being involved in Gremlin's plans. He berates Birdway for not talking to him and trying to seek other options. He doesn't say using logic to save people is wrong, he says that without emotion logically there is no reason to save people when in the end they'll die anyway.
And yeah, Othinus came out in Baggage City to destroy Dainsleaf but also to see what was inside Touma's right arm and then kill him to try to move Imagine Breaker to another, less troublesome host, as Ollerus and Fiamma said. Why would she come out only to destroy Dainsleif when Touma was already going to do so?
Touma is not a death seeker, he clearly doesn't believe in it (as he told Fraulein in this volume and Mikoto in the sisters arc). He makes the point that normal people will want to save someone if they can and he has power to do it, so, why shouldn't he? From the start of the series Touma has been a person who helps everyone, friends, strangers and even former villains if he can. He doesn't need a reason to save someone.