Because they view every interaction between men and women as competition rather than cooperative. Feminists compete in order to maintain the majority if not the entirety of resources for women and only women when it comes to domestic violence as well as other areas of government funded programs such as mental health which the majority of its funding goes to women's issues as well...*cough* you helped cause male school shooters *cough*
Also another reason as to why they do not allow men in to domestic violence shelters is because it would ruin the narrative that "men bad, women good" as the founder of one of the first domestic violence shelters Erin Pizzey noted "I found that often times domestic violence between men and women was reciprocal" as well as going on to say that she observed from those who came in that the majority of those who instigate domestic violence were women. For this early feminists ran her out of house and home as she had to move after bomb threats and the slaying of her dog.
Also another growing reason as to why they do not want men going to domestic violence shelters is because it stands the risk of having FEMINIST WOMEN themselves being outed as abusers. It is widely known that the majority of modern day feminists, especially those embroiled in social justice and intersectional feminism, are notorious for the rampant amount of emotional and psychological abuse they visit onto their male 'partners' and while physical violence is considerably rare it is not unheard of.
This rampant amount of abuse is probably due to a shared cognitive dissonance that either what they are doing is not abuse, even though if a man would do the same to them they would consider it as such, or that they are not capable of committing abuse towards their male 'partners' because that is something only men do. This has earned them much infamy within the dating world and are essentially avoided at all costs, even when it comes to one night stands, that most men refuse to date them period or do so like someone trying to cross an active minefield which is a prospect in and of itself something that would cause stress related health concerns and yet another reason as to not date/marry/have sex with them at all.