Before I directly address the topic of this post, I feel compelled to re-iterate how completely ridiculous the plot thread was in AvX where somehow Spiderman is more qualified than Cable to train Hope in handling the Phoenix. Even Keiron Gillen acknowledged in a recent interview that the legitimacy of that whole set-up was questionable. Cable was raised by Rachel Summers, aka The Phoenix, so I'd imagine he'd have a thing or two to say on the subject. And before you say "well, Peter was really just teaching her the old great power/responsibility" spiel, I find it extremely unlikely that this was not pounded into her skull every single day of her life by a man who has possessed God-level powers and knows exactly the cost of one's actions.
All that aside, the real crux of the issue here is that Cable trained Hope her entire life, and when the time came for her to live up to her father's legacy, she balked. Faced with the Phoenix-force on the moon, she just caved and suddenly became an insecure teenager (Hope's characterization has wildly fluctuated over the years, so I guess it's no surprise she see-saws between hardened survivor and typically clueless teenager, but still.....) She had the opportunity to make her father proud and instead she royally screwed it up. Now, okay fine, Marvel...you want your teenage audience to identify with Hope, I get it..... but you know what happens when children fail to live up to their parents' expectations? Generally the parents are kinda disappointed. So I guess it just kinda upsets me to see Hope getting all mad at Cable for....what exactly? Letting her live her own life? But anyway, she gets to be mad at him, and he just takes it all in stride, with nary a word of "hey kid, you really forgot everything I ever taught you right when it counted most...I'm quite disappointed in you." In fact, throughout this constant back and forth argument of "Scott was right....No Cap was right!!!!" nobody seems to be assigning any blame at all to Hope. I would really just like Dennis Hopeless to have the Cable/Hope dynamic in CAXF a little less rosy and a little more complex.