Just watched ep. 13 in subs. Fairly more detailed on MaiXTate relationships as expected from reading this thread.
It seems more like Tate is Mai's life on the line person cause the way he reacted isn't like a common jealousy one, more like a so call heart attack about to outburst, and from the way both react after Rei-san accusing them together, there's no doubt that they like each other. Anyone also see the way it looks when Mai n Reito was about to kiss, it seems more like Mai got drawn to him than she wants to. Like a spell cast on someone to control them
Although I didn't see how can Tate's point be dropped in this episode, when he was hurting Shiho, its more like he couldn't control himself, as what I think affects a person's love one when other's still confuse about themselve. Like i.e., if the show's about the love one gets affected by the HiME's power, it can also be affected by her feelings, as someone mention before that it's destiny that they already pair them up as it is, if she still confuse on who she likes and go for the wrong one, the right one would likely get affected, so thats how I see in this episode revolving Tate.
edit: Mistaked for another show, damn, I need glasses.