@Nixnaw That's an interesting way of looking at it. When she said "家族を許すつもりもないよ/nor do I plan on forgiving my family", I hadn't thought too much about what beef she had with her family, whoever her family is. I just assumed it was some problem she had with them, but didn't think it had anything to do with her being able to transform in particular.
She has the same expression on her face at the end of "A Nekomata's Lesson II" (
here), which I at the time chalked up to envy, a "student surpassing the master" kinda deal. But knowing about her family situation, it might just be envy at the praise Buchio's getting from his family, and the praise she didn't get from hers.
As for "アイツとアタシは正反対/he and I are polar opposites", I hadn't read in the context of the following lines. I just assumed it referred to their respective personalities. But taking the whole conversation into perspective, interpreting it as "He and I both developed powers, and we both had to face our families, but when it came down to it, his family accepted him and mine didn't." is totally valid.