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President Coin is one of the few characters given a lengthy physical description in this book:
She's fifty or so, with gray hair that falls in an unbroken sheet to her shoulders. […] Her eyes are gray, but not like those of people from the Seam. They're very pale, as if almost all the color has been sucked out of them. The color of slush that you wish would melt away. (1.27)
Coin is described in a variety of light (and unpleasant) colors: gray, pale, slush. Katniss says it's like "all the color has been sucked out." Coin is an ominous blank. Maybe this is a reference to that other leader who references whiteness, President Snow.
Alma Coin's name is also troubling when we stop to analyze it: "Coin" can be an obvious reference to money, but "Alma" means "soul". It's almost like she has a soul made of money – she's moved by hard cash rather than feelings. As such, she's probably somebody not to be trusted.
Katniss realizes early on that Coin has the potential to be a big adversary for her. Katniss has dealt with plenty of enemies and authority figures, but there's something different about Coin:
[…] [President Coin] has been the quickest to determine that I have an agenda of my own and am therefore not to be trusted. She has been the first to publicly brand me as a threat. (5.1)
If Katniss is a danger to Coin, Coin's a danger to Katniss as well. It's not enough for Katniss to be fighting against the Capitol, then; she also has to be prepared for a sneak attack from the leader of the rebels.
Near the end of the book, we're horrified to hear the following suggestion from Coin:
"What has been proposed is that in lieu of eliminating the entire Capitol population, we have a final, symbolic Hunger Games, using the children directly related to those who held the most power." (26.47)
When pressed by Haymitch to disclose whose suggestion this actually was, Coin cops to it freely: "It was mine [my idea]. […] It seemed to balance the need for vengeance with the least loss of life. You [the victors] may cast your votes" (26.53). Katniss was right about Coin being dangerous, she just didn't realize how cold and untrustworthy Coin actually was.
Coin's remarks here also help Katniss make sense of the shocking reveal Snow made. Snow said Coin was primed to become a despotic ruler of Panem all along – that she'd used the rebels and the Capitol to tear each other down so she could move in and take control. It sounds like her first act of power will be to exactly replicate one of the main things the rebels were fighting against: the Hunger Games. In that light, her assassination almost seems – how should we say this? OK, we'll just say it – deserved.