So I've been seeing this as a criticism against the movie. How when Jean was able to possess Frank and see his memories, she comments that he has issues. People seem to think she's making light of what he went through and wondered why she didn't sympathize with him, when Peter's memory of Aunt May was able to stop her. 

I believe that's because after seeing Frank's memories, all Jean got from it was validation for her actions. Frank went on a murder spree when his family was killed and he slaughtered as many people responsible for it and those who got in his way as possible. Jean was tearing through the city and Damage Control to get her sister back and find whatever V-Max was, so seeing someone infamous like the Punisher choosing to, what she believed, do the same actions she was doing, made her think her actions were completely justified. That if someone took your loved ones, you have every right to retaliate in any manner to get them back or get back at those who took them. 

She would also see the mental issues he had especially during One Last Kill when he was seeing hallucinations and voices in his head. So she wasn't making a joke, she was completely genuine when she said that, Frank does in fact have issues. 

Compared to Peter, the first person she ever met whose mind that she couldn't enter. She was very interested and desperate to get in there because he was always getting in her way and nobody was able to keep her out before. When she finally gets access to his mind after he lets her in, she wants to use what he had against him for her advantage, like what she did with MJ. But what she found was the memory of Aunt May talking to him about being Spider-Man and accepting that. 

One of the biggest reasons Jean was the way she is goes all the way back to when she and Sara were thrown out by their mother due to their powers developing. This caused a huge effect on Jean's mental state, making her think no one except her sister would accept her because she's a "monster". They used their powers however they pleased since no one was able to guide them on how to use them responsibly. It's why Jean has no qualms with the collateral and casualties she causes in the movie, people are calling her a monster and will want to hurt her or lock her up regardless, so why should she care about any of them?

When she finally sees that memory of Aunt May that Peter was keeping close to him, she sees not only what has been driving him to keep being Spider-Man despite how lonely and isolated he was, she saw he had the things she never got: **Love and Acceptance**. Someone who could see all she has and could be, still love them for who they are, not what they are. And since she's connected to Peter's mind, she could feel the genuine love May was showing to him which is why she took Peter's place in the memory: **She wanted to feel what it was like for someone to love her for who she was, not be afraid of what she was.**

**That's why Jean stopped fighting him after seeing that, because Peter lost someone so important to him, but unlike Frank, he was able to not let himself be lost in hate and rage. He spent the last four years as Spider-Man since then not for the sake of glory, or recognition, but to live up to what May believed he could be. A Hero.** 

Jean Grey and Frank Castle's relationship: Why Frank's memories didn't move her but Peter's (or more specifically Aunt May) did