The Archbishop of Manila, is not responsible for the Catholic Church in the Philippines. This honor goes to the head of the Catholic Bishops' Conference of the Philippines. In theory, the Archbishop of Manila is just the head of one of many many archdioceses in the Philippines.
However, whoever is in this position has been traditionally the most prominent, and most influential religious leader in the country. Throughout history, the person in this position had been strongly involved in the issues of the day. One had a hand in the murder of a Spanish governor-general. Another was a key player in the EDSA revolution.
The current Archbishop of Manila is Jaime Cardinal Sin.