The Catholic Church did not used to allow girls or women to be altar servers. In his Allatae Sunt on July 26, 1755 Pope Benedict XIV explicitly cited Pope Innocent IV:
Women should not dare to serve at the altar; they should be altogether refused this ministry.
He also referenced Pope Gelasius who stated that women serving at the altar was one of the "great evils" which had spread during his time.
In Canon 230, the Code of Canon Law reserves the role of acolyte, one who lights the candles in the Mass and prepares the Mass before the procession, to men. It is only in the necessary absence of acolytes, who are in fact clerics-in-training themselves, that 'altar boys' were permitted as temporary 'fill-ins'. These 'altar boys' were truly not 'boys' though, but rather typically adult laymen. The need of these temporary laymen was relevant during the Middle Ages in which clerics were attending seminary schools and were as such not able to assist the priest with preparing the Mass.
Due to the changing of times, the system of seminary schools has changed, and 'minor orders', to which clerics-in-training were devoted, passed somewhere into the abyss of times lost. While the participation of laypeople, as in laymen, in the Mass might have persisted for quite sometime, it is only of late, around the 1960's actually, that certain churches simply started to include girl altar servers not as in an act of need, but as in an act of regularity. The Vatican responded disapprovingly with the text Liturgicae instaurationes, written in the 1970. Despite this exercise of clarification, many churches still insisted on the practice, and so in 1980 the Vatican again affirmed a traditional position on the matter in the 1980 Inaestimabile donum. Granted the absence of the traditional 'minor orders' and the traditional definition of a 'cleric', the secularization of the Church urged Church leaders to interpret differently Canon 230, as though it were providing room for the inclusion of women in the liturgy as a regular practice. Not taking such a drastic step, which would be misinterpreting the role of laypeople in the Mass,the Pontificial Council for the Interpretation of Legislative Texts (it's a mouthful, I know) was submitted a doubt in the common interpretation of Canon 230. It was to this official council that the Canon would be left to interpretation. The Canon to be discussed, Canon 230.2, read as the following:
Lay persons can fulfill the function of lector in liturgical actions by temporary designation. All lay persons can also perform the functions of commentator or cantor, or other functions, according to the norm of law
Traditionally, 'other functions' did not include altar serving, and if so, only in the most odd of cases. But the Council found otherwise. Furthermore, that the Latin term 'laici' used in the second paragraph in reference to the various functions that could be performed was in contrast to 'viri laici' used in the first paragraph to refer to the official titles of acolyte and lector implied that the former was referring specifically to men while the latter was referring to all laypersons, including women. So it was that the 'official' stance regarding whether women can be involved in altar serving became a definitive 'yes'. But the Council left such a decision ultimately up to the bishops. Furthermore, Church leaders including St. John Paul II and Pope Benedict continued to express support for traditional Mass rites rather than the contenporary practice. What is interesting is the progression of how girls came to be altar servers. The Church went from official clerics as the assistants of the priest, to layperson men, to layperson boys, to finally layperson girls.
Many traditionalists argue that laypeople serving Mass and fulfilling the roles of lector, cantors, and acolytes (the list goes on) were not intended by the early Church. If one reads the Canon one in fact finds that such instances were expressed as being only present when the Church did not have available official clerics present, who were likely in training to be priests. As such, many traditionalists interpret the Canon as being inherently conditionally true, in which such examples, laypeoples' roles are only in cases of great need. But the modern churches, now with little resistance from Pope Francis, quite obviously participate in such practices as though they were always meant to be regular, and if not, that are at least to be considered regular now. Only two diocese in the United States currently do not allow women participation in the process of Mass, and they are often looked at funny. For this reason, this issue has caused somewhat of a divide in the Church with several Catholics becoming perhaps overly zealous traditionalists and other Catholics becoming perhaps overly willing seculars.