It's pretty simple: you're against the idea of someone being executed so callously (for moral or pragmatic reasons). When you DO but in to the conversation, you NEVER tell her how to do her job. You just ask her - forcefully - why she's ordering this person's death.
But the options you, as the player, are presented with are to either stop the death of the murderous traitor or to allow it. The choice comes before the investigates.
If you think people shouldn't be executed on a whim, then you speak up. There needs to be no more justification than that fact.
Whim? He's a traitor who has caused the death of one of your allies and is a threat to others. His execution may not meet modern standards, but it's definitely one of the more justifiable deaths out there.
I mean, you just came back from slaughtering a whole bunch of mages for no particular crime beyond hanging about in the hinterlands. You're soon going to go out to kill a whole bunch of people later. You'll likely soon recruit Sera after she orchestrates your slaughter of a whole bunch of other people who have committed no apparent crime except defending themselves from the assault of your heavily armed cronies. But no, it's this traitor guy who is special and need saving, apparently.
The whole scene - if you speak up - is about you *asserting* your beliefs. You do this each time with Leliana. It's completely divorced from your role as a member (or leader) of the Inquisition.
But there's no particular reason why this occasion should require you to speak up, unless your beliefs are frankly incompatible with playing the role of Inquisitor throughout the game.
It's not any different when you get made Inquisitor. You didn't have a say OR command over Leliana when she called her scouts back. She's wrestling more visibly with the moral weight of her choice. And you - as the Inquisitor - start to opine on the moral value of her choice (whether it was right or wrong).
But that time, Leliana is asking for your opinion which is quite different.
Though that choice is stupid too. Either you're a callous bastard, or you have no idea how military strategy works.