As Cardinal Joseph Ratzinger and as Pope Benedict XVI, the former Cardinal, now Holy Father, has always taught that Vatican II never abolished the older form of the Mass, now known as the Extraordinary Form of the one Roman Rite. Vatican II did not reform the now known Ordinary Form of the Roman Rite either, it simply put forth principles which would guide the proper authorities to reform the Mass, but under the authority of the pope. In this sense, Vatican II ushered in an era where there could co-exist the two forms of the one Roman Rite which at the time and even today is considered a "novelty of renewal" brought about by Vatican II as a gift to the Church with little precedence in Church history.
This is what Cardinal Ratzinger said:
It is of course possible that in this area there are reasons which are anterior to any theology and which have their origin in the individual characters of people or in the conflict between different characters, or even in other entirely exterior circumstances. But it is certain that there are also deeper reasons which explain these problems. The two reasons one most often hears are: the lack of obedience to the Council, which is said to have reformed the liturgical books; and the disruption of Church unity, which is said to follow necessarily if one allows the use of different liturgical forms. read...