It is hard to say why you were arrested based on the facts you provide. However, it may have something to do with the fact that you went over to his house so the police assumed you instigated the fight. I assume that he and his girlfriend told the police that you did and they believed him over your story.
The most important thing for you do to now is protect yourself against a likely Motion for custody and visitation. If he sought a domestic violence restraining order and obtained a TRO, then you need to hire an experienced family law attorney to represent you. I am including links below that will help you understand the implications of having a domestic violence restraining order against you as it relates to custody. Good luck.
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No one on this forum can tell you why the cops arrested you.
You need an attorney.
The above is not intended as legal advice. The response does not constitute the creation of an attorney client relationship as this forum does not provide for a confidential communication.
You should request a copy of the arrest report. There should be a detailed narrative portion in which the arresting officer sets forth the basis for the arrest.