There are major problems with the Turnaway Study.
In short, given the fact that 62 percent of the women that ANSIRH approached refused to be interviewed and an additional 37 percent of the initial participants subsequently dropped out before the critical third-year interview, ANSIRH researchers simply have no reliable information about what “most women” believe regarding their abortion decisions.
With such high nonparticipation rates, the likelihood that the results are biased by self-selection is clearly high. Buried in the details of their paper, even ANSIRH admits that women who reported the highest rates of relief and happiness at the baseline interview eight days after their abortions were most likely to remain in the study (Rocca et al. 2015). Conversely, the women who reported the least relief (and presumably the most negative feelings) eight days after their abortions were most likely to drop out before the three-year assessment of their decision satisfaction.
Numerous studies have also confirmed what common sense suggests: the women who anticipate and experience the most negative reactions to abortion are the least likely to want to participate in interviews that stir up their negative feelings (Adler 1976; Söderberg, Andersson, et al. 1998). It is also known that women who anticipate more negative feelings about their abortions actually do experience more negative feelings (Major et al. 1998). It follows that women refusing to participate in postabortion surveys sponsored by their abortion clinics are accurately anticipating that they do not want the stress of interviews that are likely to stir up their negative feelings.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6161227/Even if you believe the study design is okay and is a representative sample, the claim that it doesn't increase depression and other mental health issues is in comparison to those who were prevented from having an abortion. So if you are using this research to say that abortion doesn't cause mental and emotional problems, you have to say the same thing about laws that deny people the ability to get abortions.
First of all, of course, the same study that found that, five years later, 99% of women did not regret their abortions also found that 96% of women no longer wished they’d had an abortion. Taken together, it sounds as if most people come to process and accept what’s already happened no matter which way it goes. (Research about lottery winners and people paralyzed in accidents seems to confirm this idea – their overall happiness doesn’t ultimately change as much as you’d expect.)
https://secularprolife.org/2021/03/five-years-later-96-of-women-denied/