[hgsgm]

More specifically, mission control management intentionally chose to launch Challenger after being notified that the launch was rejected by engineering.

Same as Titan -- Management intentionally launched into catastrophe. At least Rush bet his own life on it, not only innocent victims.

I'm not sure about Colombia.

[nocoiner]

With Columbia, Mission Control knew there was a potential issue pretty much as soon as the shuttle reached orbit, but because there was basically nothing* that could be done about it, they essentially were going to not worry the crew too much about it and hope for the best. As I recall, they modified the reentry procedure somewhat to possibly reduce stress on the affected wing. Obviously it did not work.

* There were a handful of high-risk options that in all probability would have resulted in one or more dead astronauts. One plan would have been to send the Columbia crew on a spacewalk to try to fashion whatever kind of shield they could jerry-rig to cover the ceramic tiles - like bags of frozen water. The most glorious plan would have been putting the Columbia crew on a minimal sustenance/activity schedule right away and then rushing the next orbiter scheduled to fly (Atlantis, I think it was) into orbit on a rescue mission. I get chills even thinking about that kind of mission, but the shuttle was obviously a temperamental vehicle, and if NASA had cut the normal months of prep time into a handful of weeks, who knows what could have gone wrong with that launch. I have no doubt you would have had 100 or more volunteers among the past and present astronaut corps to fly it though.