I'm going to try to make one slight change to my Miyanaga Sisters Estrangement Theory (as posted
here) to account for the key flaw I've seen brought up against it - The flaw being that Saki talked about how her family also got upset when she
won.
To fully explain this alternation, I think it might be helpful to draw a comparison between the Miyanga Sisters and
the Williams Sisters of real life Pro Tennis.
The Williams Sisters were completely dominant in women's pro tennis for about a decade. Over that decade, though, there was much controversy surrounding them due to how their father (and coach) managed them. Basically, there was widespread speculation that Richard Williams was fixing at least some of the matches between his two daughters - There was a sense that he felt that one tournament was "Venus' time to shine" and another tournament was "Serena's time to shine". Now, this was never proven, of course, but suspicions were there.
Now, what if the father of the Miyanaga sisters was like that? What if he felt that Teru should get to be dominant first since she's the older sister? So he
privately got upset with Saki when she defeated Teru a couple times. So Saki decided to use the plus/minus zero approach to ensure that Teru didn't lose to her. While this pleased Saki's father, it enraged her mother, and Teru also took great offense at Saki throwing matches like this. This ultimately tore the family in half.
Saki's father eventually goes on to regret his complaints to Saki, but he thinks it's too late to fix things. He goes on to feel bitterness towards mahjong because of it. Teru might not have known that her father encouraged Saki to throw matches, and so all of her anger is understandably focused on Saki. Saki cares for her father, so she doesn't want to blame him for this, so Teru is never told the truth about it.
My theory might not need this alteration, but I think I'll throw it out there just to answer the "They also didn't want Saki to win, though" hole in my theory.