My thoughts about this comes from my own experiences. I believe most times an argument is started because one person in the relationship feels hurt, threatened, betrayed, misunderstood or alone and as they try to convey those feelings the other person is then feels on the defensive, angry, upset, hurt and words are starting to be exchanged. I am certain in most cases the communication was not meant to start an argument but it is the result of the situation.
But there are cases where the person is just trying to get under your skin. Or they like to argue with you. Those kinds of situations are usually unavoidable unless you leave this type of relationship.
So to answer your question, I would say I do not believe there is one gender over the other which starts the argument.