Many of the reasons are explain in
Sacrosanctum Concilium, which I linked to above. You may also want to take a look at Paul VI’s,
apostolic constitution on the promulgation of the new Order of Mass.
Basically, there were a number of things in the liturgy that had been frozen in place since the 1570s, which, with the hindsight of four hundred years, it was thought could be changed. For instance, at the old Mass, the readings were in Latin and usually not spoken toward the congregation. If a priest felt like it, he could repeat the readings in English during his homily, but he could just as easily not (often at daily Masses priests just omitted the homily, along with the English repetition of the readings, altogether). And the readings didn’t cover a very broad scope of the Bible either; the Old Testament barely got mentioned at all (you can see a very interesting breakdown of the old and new lectionaries
here). By the 20th century, many people in the Church had come to a different understanding of what the purpose of the readings is than was held in the middle ages: it is so that the people can hear and learn the teachings of the Bible.
That’s one example of the type of thing they were concerned with. There had been moves toward other changes in earlier decades, too. So, for instance, in the old Mass, the priest says the Our Father by himself, the people are not supposed to join in. Many people thought that this well-loved prayer could be opened up for the congregation to join in it, and in fact in many places this had already become standard practice. In 1958 (in the document
De Musica Sacra), the Holy See under Pope Pius XII confirmed that this practice was permissible, at least in low Masses. This followed up on other changes in the 1920s that similarly allowed greater congregational participation in some of the responses, which otherwise would be reserved to the ministers and usually not even audible.
I can’t give an exhaustive list of everything that the Church thought was of importance in revising the Mass, and I’m sure there were different views from bishop to bishop among the Council fathers. When you look at the history of the movement to revise the liturgy and the things they were concerned with, though, it has to do with the
Catholics in the pews – should they be able to hear the readings? and from the Old Testament? should they be able to join in the responses? in the singing? – and has essentially nothing to do with thoughts about what would be appealing to Protestants.