Why on earth did Coin and the rebels assume Katniss was in love with Gale
Because of the lack of freedom of speech and the capitol's indoctrination in the districts, most people do not see through the "star crossed lovers of district 12," and either believe or have to believe that katniss and Peeta truly fell in love with eachother in the games because that is what is portrayed.
Whereas, the people of district 13 are more aware of the capitol's tactics and hand in what is shown on the screens, and are able to piece together better that these are two children putting on a show for Panem.
Katniss assumes they are aware of it just being a show because of her "bad acting," but the fact that she had not only the Capitol and President Snow but all the districts except 13 fooled (as we saw when she visited the survivors in the hospital in 8, who asked her about Peeta and the baby) shows that she did a pretty good job.
Only the other victors (who were also aware of the Capitol's deception) suspected it being a fraud. But even the other victors who know it is a show, are aware that katniss still cares for Peeta. And that she does love him deeply in her own way when they see her in the quell with him.
Until, we get to scene where katniss relays her conditions to be the mockingjay to coin, where they not only assume that she has basically had 0 feelings for him during the whole thing, but also that she was in love with Gale.
And that makes us wonder, what made them think that? Is it just Coin and her gang, or is it all of district 13 who think she has no feelings for Peeta at all and is infact in love with Gale, who is only seen alongside her in public.
Why think that when they know that she went hysterical and clawed haymitch's face when she found out Peeta was left behind in the area. There's also the fact that she casually caressed the screen that showed Peeta on his first interview with caesar infront of all of district 13. And the fact that she literally just made out passionately with him in her underwear during the quarter quell infront of the whole country to see.
Assuming she’s not in love with Peeta is one thing, but thinking she’s in love with Gale? Where the hell did they get that from??