Crying has everything to do with infanticide.
It also lowers male aggression, which protected babies from infanticide. Here come angry papa responding to the baby alarm!
In most primates, males commit the most infanticide. Humans are the exception. Infants are almost never killed by men. Women often kill their own newborn out of severe trauma. Though some kidnap and kill out of jelousy. Never trust a woman having a hard time getting pregnant. Never let her near your pregnant wife. Never let them alone with your newborn or young child.
Killing your own offspring out of spite is a very useful evolutionary advantage in species that need to put a lot of energy in their kids. Male forced you and fertilized your eggs? Just recycle and start over next time. In humans, it means not putting years of energy into a child forced on you. Kill and start over with a stable partner. Because of this, rape is only about seeking dominance and control over someone. It has nothing to do with reproduction anymore. Men commit more sexual assaults than women, but the motivation behind rape is the same. Women may be less violent, but still often torture their victims in other ways.
Adding factor is serial monogamy. Animals who lost their partner, are willing to neglect their offspring to increase their bond with the new mate when he/she doesn’t accept their offspring. Humans do this too. The cold stepparent.
Baby killing is a natural behaviour. Albeit a horrid one. It’s a way to maintain bodily autonomy for females in general, and especially useful when two parents are more succesful than a single parent. Menstruation made it so that infanticide would be even less likely. Menstruation reduces the chance of pregnancy by 40-60%. It’s a preventive misscarriage known as embryonic wasting.
The defensive behaviour of reducing male aggression led to women crying more than men. Baby cries don’t lower women’s aggression. It might increase it. The smell of babies for sure increases female aggression. Mostly to protect their child from a jelous/grieving female who lost their baby (female-female competition is understudied) or from a controlling male bachelor looking to get the mother to ovulate again sooner so he can mate with her (with or without consent!).
Not saying you shouldn’t be nice.