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Sure, but again, saying she had a skewed life that set her on the wrong path is accurate and explains the why and sure, she becomes a more relatable and sympathetic character when you can understand the conditions of her life that helped set her on the wrong path.  You can even see a sort of valid logic to her decisions, given what her experiences in life have been.
But objectively speaking, if we’re judging someone, traumatic upbringing or not, her choices and actions are objectively shitty.  I think that’s partly what makes her such an unfortunate character.  You can see why she had some things working against her that would have skewed her life and feel a bit of sympathy for her,  like “this poor girl never had a chance”, but she so did what she did and has to own that.
Let’s us an extreme example to make a point.  Let’s say someone was brought up by a murderer, who didn’t hide from the family that they were a murderer.  The, the youth, sensed it was wrong, sensed it bad, but had no power to change or stop it.  So they grow, they move on from their parental unit because they know it’s a terrible place to be.
Whether through choice or through conditioning, or some combination of the two, they then take to assaulting others.  Mind you not killing, but assaulting.  On the one hand that person could be like “well at least I’m not my father” and you might even be able to understand that to someone brought up is such a traumatic fashion would normalize violence and so you can understand how they wouldn’t have the emotional development to refrain from some level of the violence they were raised in.  They may have been taught that it’s ok to kill someone who does you wrong, but this person is like “no, I won’t be like that”, so instead, in their skewed version of reality a beating isn’t that bad. 
You could understand why someone who got raised in a fucked up environment might think this way, doesn’t mean you agree, but you could understand that and you could reason it all out, again not justify it, but explain it all from a clinical sense.  But my point is that while you might be right that this persons trauma set them up for failure and that at least they aren’t the monster their dad was, objectively speaking, fucked up childhood or not, this persons behavior and perspective in reality is still messed up and dangerous.  You can sympathize with them for that even, but they’re objectively bad.
That’s an extreme example, but the point is that even through someone might not be the cause of their trauma, they’re still ultimately responsible for their choices and how they behave.
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Jenny was sexually abused by her dad.
Forrest shows up, and after having sex, she feels like she might have done the same thing to Forrest. In her mind, she sexually abused Forrest because he is not mentally capable of consenting. Do you see the parallel there?
That's the root of her internal conflict. She's terrified she's going to become her father and continue his cycle of abuse.
She eventually comes to realize that Forrest is more capable than she thought. However, she's a walking bomb of self-destruction at this point, and she knows it.
With the last ounce of selflessness she could muster, she leaves her child with Forrest. It was painful for her to lose the only two people who still love her, but any other action would ruin the child's life. At least, this is what she believes.
In the end, Jenny is a selfish and destructive person, but she abandoned love itself in order to save her child from her cycle of abuse. >

For the most part I agree with what you're saying, but what you're saying is the explanation for why she did the things she did, not justification for those things.
Someone can have really shitty reasons to do a good thing and really good reasons to do a shitty thing, but the end result is whatever actions were taken.  "Perception is reality" and "actions speak louder than words" basically, because ultimately we can't get in to other peoples heads for the exact reasons or motivations why they did something.  Sure we can guess, even take an educated guess if you know the person well and/or are a mental health professional, but no one except the person who's the subject, really knows the exact details of why someone does a particular thing.
The reasons explain the why, but they don't necessarily justify the actions.  Outside of her relationship with Forrest, Jenny continually makes really bad life choices and shows her self as someone who doesn't seem to place much value in others or herself.  So when you combine those actions with how she treats Forrest, while she may have reasons to do the things she does, the things she does are still ultimately pretty shitty. >

When a child is abused, it's much worse than an adult's excuse or a bad habit.
The abuse becomes normalized. Only strong minds are even able to recognize that their "normal" is wrong.
Most often, the child grows into an adult who doesn't know what a normal life should be nor how to achieve it. They have children, and the cycle continues.
Jenny continuously made bad choices. Yes. She never learned what choices were good.
It was never her excuse for bad choices. She tried making the right choices, but with a broken compass, she never had a chance.