The feast was introduced to complement the celebration of St. Michael on September 29.
Why Catholics celebrate Guardian Angels on October 2? In the current liturgical calendar, there exists two feasts that honor angels. The first is the feast of Sts. Michael, Gabriel and Raphael, celebrated on September 29. Initially, it celebrated only St. Michael and it was also a day of obligation.
Eventually there arose a request to have a separate feast in honor of the guardian angels, those angelic spirits that are assigned by God to guide and protect each human soul.
According to the Catholic Encyclopedia, October 2 was picked because it was the first “free” day in the calendar.
It is believed that the new feast was intended to be a kind of supplement to the Feast of St. Michael, since the Church honored on that day (29 September) the memory of all the angels as well as the memory of St. Michael. Among the numerous changes made in the calendar by Clement X [in the 17th century] was the elevation of the Feast of Guardian Angels to the rank of an obligatory double for the whole Church to be kept on October 2, this being the first unoccupied day after the feast of St. Michael.
At the time it was chosen, September 30 was the celebration of St. Jerome and October 1 was the commemoration of St. Remigius, patron saint of France. October 2 did not have any particular celebrations and so it became the feast of the Holy Guardian Angels.