Is the site legit? Do you think the site is rigged? Was there any similar complains before? Are you sure you placed your bet on the right team. Well honestly, if the site is legit and not rigged, then there is nothing you can do or the support. There is not way you can prove that you placed the bet on Team A. The support probably gets shit loads of messages from scammers that claim there was a mistake from their side after (after losing a bet). All i would say is just move on and don't waste your time.
Fairlay is legit i've used their betting exchange multiple times. Their UI could be confusing if its his first time betting with an exchange but for the most part it shouldn't be when there's only 2 options (bet on and against). I think what happened with OP is that he clicked the button quickly too many times or accidentally fat fingered it causing his bet to switch if the bet was made from the phone.