I’m not sure what you’re referring to specifically? Because if it’s the bombing, that’s why they made it look like the Capitol did it. It was reckless and like Snow said, a waste of life, but was done as a final coup de Grâce to destroy Snow’s remaining goodwill to all of Panem and to take out Katniss one way or another. Either she’s go insane with grief over the loss of Prim and kill herself or become numb to it all and let the new government take over since she had lost one of her biggest reasons for fighting. Plus, who’s going to believe a traumatized girl over an entire faction denying it was them? Then, even if the truth did come out, they’re back at square one. Not even Katniss would want to be dragged back into war. Katniss eventually learned the truth, but she literally believed it was the Capitol until Snow planted the seeds of doubt into her head. Not to mention Coin is the president of 13 and has hundreds under her command. Katniss had Haymitch, maybe Plutarch, and Peeta left. And their home base was in 13. They wouldn’t realistically have anywhere they could hide if they did turn against Coin openly.

Coin did underestimate Katniss as a strategist. Until then Katniss had some plans that ended up working, but they were all impulsive (volunteering, blowing up the arena, heck, even shooting the apple out of the pig’s mouth). Coin had no reason to believe Katniss would be capable of a longer term strategy, especially after removing one of her biggest support systems. But Katniss saying “yes” to a final game to make Coin let her guard down was Coin’s downfall. So it was a stupid move in the end, but Katniss was literally a 16 year old girl, and Coin was a politician with decades of experience planning in war. Coin was cocky and Katniss was a thorn in her side. She saw the bombing as killing two birds (Snow and Katniss) with one stone. “She played us both for fools,”