I clearly don't understand the motivation for President snow of the Hunger Games: Mockingjay and the leader of the Capitol (Capital) to hurt Katniss Everdeen by using Peeta on screen and getting Peeta to say all these things about a ceasefire but when the rescue team from District 13 go to the Capitol and rescue some remaining tributes from the Hunger Games that have been held ransom, they are helped out by some supporters in the Capital itself. But when they get Peeta back to 13, he attacks Katnis by strangling her.
Why would President Snow just let Peeta be captured by District 13 rescuers and let 13 take him? Also to add: why would Peeta have saved 13 from the bombing from the Capital and basically saves them, when he is rescued he attacks her? what is going on here?