You're missing the point - whether or not promiscuity leads to mental illness, or mentally ill people are more likely to have more sexual partners, the relationship is still there. It's probably a combination of both, but I would still propose that oxytocin is a moderating variable.
But, since you're too lazy to read the studies and are more interested in digging your heels in, with no evidence to support your claims I'll just quote walls of text.
https://www.apa.org/monitor/2013/02/sexual-hookup-culture.pdf
Hookup Culture and Psychological Well-Being
"An individual history of hookup behavior has been associated
with a variety of mental health factors. In a recent study of 394
young adults followed across a university semester, those participants with more depressive symptoms and greater feelings of
loneliness who engaged in penetrative sex hookups subsequently
reported a reduction in both depressive symptoms and feelings of
loneliness (Owen et al., 2011). At the same time, those participants
who reported less depressive symptoms and fewer feelings of
loneliness who engaged in penetrative sex hookups subsequently
reported an increase in both depressive symptoms and feelings of
loneliness (Owen et al., 2011). In another study, among 291sexually experienced individuals, those who had the most regret
after uncommitted sex also had more symptoms of depression than
those who had no regret (Welsh et al., 2006). However, in the same
sample, women’s but not men’s degree of depressive symptoms
increased with number of previous sex partners within the last year
(Welsh et al., 2006). In the first study to investigate the issue of
self-esteem and hookups, both men and women who had ever
engaged in an uncommitted sexual encounter had lower overall
self-esteem scores compared to those without uncommitted sexual
experiences (Paul et al., 2000). The potential causal direction of
the relationship between self-esteem and uncommitted sex is yet
unclear (Paul et al., 2000; Fielder & Carey, 2010b).
A few paragraphs down -
"Qualitative descriptions of hookups reveal relative gender differences in terms of feelings afterward, with women displaying
more negative reactions than men (Paul & Hayes, 2002). This is
also consistent with earlier work demonstrating a gender difference, with women generally identifying more emotional involvement in seemingly “low investment” (i.e., uncommitted) sexual
encounters than men (Townsend, 1995). Moreover, in a study of
140 (109 female, 31 male) first-semester undergraduates, women,
but not men, who had engaged in penetrative intercourse during a
hookup showed higher rates of mental distress (Fielder & Carey,
2010b). Possibly contributing to findings on gender differences in
thoughts of worry, in a sample of 507 undergraduate students,
more women than men leaned toward a relationship outcome
following a hookup. Only 4.4% of men and 8.2% of women
(6.45% of participants) expected a traditional romantic relationship
as an outcome, while 29% of men and 42.9% of women (36.57%
of participants) ideally wanted such an outcome (Garcia & Reiber,
2008). It is possible that regret and negative consequences result
from individuals attempting to negotiate multiple desires. It is
likely that a substantial portion of emerging adults today are
compelled to publicly engage in hookups while desiring both
immediate sexual gratification and more stable romantic attachments."
Look, all I am saying is that there can be consequences to one's mental health the more promiscuous you are, and that the data shows women might experience these consequences more (again, for the biologic factors I propose). If you're smart, mental health should be a factor that one considers when choosing a mate. If promiscuity can be a good proxy for mental health, then it should be considered if you want a healthy, long-lasting relationship.
I'm not saying that women with high body counts aren't humans, but that doesn't mean people are misogynists for not wanting to date them. I don't hear anybody pouring onto women, calling them sexists for not wanting to date a guy because he's too short or doesn't make enough money (except poor, short guys), therefor it's perfectly acceptable to have standards for choosing female mates. Again, not apologizing no matter how many times you label me a "misogynist" that word has completely lost its meaning anyways.