As Kirk said to Savik, you have to learn why things work on a starship.
To be fair that was because Savik apparently didn't know about Prefix codes so they could explain them to the audience and in hindsight seems rather odd not to mention while instructing the cadets.
Even Jake pointed out that his father, with all his combat experience wouldn't have undertaken such a mission,
And Jake would probably think his father wouldn't lie to a Romulan senator and then be an accessory to his murder when he gets killed after discovering the truth, but that doesn't necessarily make that true. Seriously Sisko is a main character doing crazy stuff comes with the territory. I mean he punched Q for crying out loud.
That being said Red Squad was still a bunch of idiots. I mean it would have been one thing if the Dominion Uber ship was on its way to destroy an inhabited planet, but it was just sitting there loitering so they had plenty of time to go back get a fleet and then destroy the thing, but no they had to be glory hounds.