What's the matter with you, you feminist or something 
No, I am not a feminist. However, if I was caught saying something like this in my program, there is a good chance I would be thrown out.
When your job involves direct patient care, you are upheld to a higher standard of moral care, especially when working with patients.
The school has every right to question these students after saying something like this.
If you were a professor and you were teaching your students to be medical doctors, and you heard one of them say something like, "Oh yeah, once I become a doctor, I am going to drug my patients and fuck them," you would be ethically obligated to report them to the school.
The only difference I could see is that this was on a private FB page, so I am not sure how it would apply. Since it was said in private, does the required mandate still apply? I don't know.
However, if youre in a position of authority, and you suspect a student may have an immoral character that may harm clients, you are mandated to report them.
This is quite simple and clear in academia.