Alright, I have some time tonight so I'll out my thoughts on this matter.
At the start, she should've accepted responsibility for her actions and the child she and her boyfriend created. They should've gotten married and taken care of their child together. Given how children with both parents present in their upbringing tend to be happier and function better in society, it is the moral choice. From what I can tell, the relationship between the couple was soured over the argument surrounding the child, which should have never been an argument in the first place.
At the time of the Reddit post, things are a lot more complicated. The father had a divorce that we don't know the circumstances of, and a lot of time has passed since the couple had any relationship. For this reason, I can't say for certain that they should get back together and raise the daughter together. However, I still think the mother has a responsibility to her daughter. The moral choice is to accept partial custody of some kind.
Thing that sticks out to me here is that she didn't even want or care to see her daughter. She even demanded her name never be mentioned to her daughter. At that point, it really is just hateful and selfish. There is no justification for this.
I have seen arguments that this stance is uncompassionate towards people with PTSD, but it really doesn't have to be. Although PTSD is horrible and I would not wish it upon anyone, but there are ways to treat it without abandoning responsibilities. The argument of whether PTSD is undiagnosed, overdiagnosed, or neither can be held another day, but the truth in that issue doesn't change my thoughts here regardless.
I have also seen arguments that this stance is hypocritical given how pro-lifers are constantly arguing for adoption. If that argument includes me, it fails to understand why I (and likely many others) argue for adoption over abortion. I only argue for adoption if there is no way a person can be convinced to take care of their own child. It isn't an argument meant to convince them of the moral choice, but to simply an argument meant to convince them to avoid the worst choice. Sometimes, moral advocates have to take what they can get or they make the situation worse.
For that reason I will say this: If you absolutely will not take care of your own child, put them up for adoption. You would likely do more harm than good to your child if someone attempted to force you take care of them. Still, please try to improve yourself so that the idea of responsibility in this case doesn't repulse you.
The only other arguments in opposition to my stance I have seen are all pro-abortion arguments. Stuff like "a woman should not be forced to carry a child" and "children are saved from horrible futures by abortion" and all I can say to those are the typical anti-abortion arguments: You should've made the decision on pregnancy before having sex and you have no ability to say for certain what a future person's life is going to look like.
That about sums it up for me.