Good timing on this question because I actually replayed the reason today. In one of his social links, he brings up that watching Minako fight- it makes him feel feelings (he first describes it as angry, then irritated, finally nervous). And he even goes so far as to suggest... ask if there's any way she doesn't have to fight. The backpedals, saying it was the wrong thing to say, and of course she's working her hardest...

But Minako places a lot of responsibility on herself as leader, and takes pride in that position. She's not a battle maniac, but the idea of not fighting while everyone else is... it really doesn't sit well with her. She doesn't want to be treated like something fragile.

I'll go ahead and add to this tl;dr by explaining why this was the relationship breaker. In the Hidetoshi social link, most of the answers are- well... you say what Hidetoshi wants to hear. So that's what Minako did. And, along the way, he developed feelings for her. It was one of the first big emotional hits that Hidetoshi had fallen in love with her acting. She felt guilty. He didn't let her respond to his confession, so she made a silent promise to try and show herself more openly.

So, she diverted the link so it didn't go down the romantic path. Just, nope. I am leader, we are fighting, and we are keeping this relationship above the belt.
(...not to say I wouldn't ship it)