Amongst people of similar standing, the man is always presented to the woman. When two women (or men), the junior is presented to the senior.
Where the man is of much higher standing he would have a lady presented to him. For example, a woman would be presented to the mayor or a lord. I suspect that the relationship with one's wife means that she is presented to all others by her husband unless she is of high social standing (but I may be wrong).
This all stems from the Victorian rules and responsibilities of acquaintance. It was deemed important to gain permission to acquaint one person with another before doing so because those people would be bound by such rules thereafter. Hence the request of introduction: "Please allow me to introduce ..." or "May I introduce / present ...?" I guess that a husband would determine whether or not another should be acquainted with his wife and therefore sought to introduce her to the other.