I dunno what part of Tomo's entire existence up until this point would lead anyone - audience or character - to think that she'd be totes cool with being treated like a prize to be fought over. Let's be real, if her dad was like "Daughter, if you want to date a boy, you must first defeat him, and then me", she'd probably get super fired up for it. If it was something she was doing together with Jun, then I bet you anything she wouldn't care that they were holding off on dating, she'd just be thrilled that they could train together to take on a big challenge as a team with a cool reward waiting for them at the end of it.
Instead, she's been sidelined, without even knowing about it. Of course she's mad. Her whole fear about confessing to Jun and having him see her as a girl was that she'd stop being his bro in the process, and that's exactly what's happened. And now she can't be his bro or his girlfriend? I'd be pissed off, too.