The document that relaxed fasting obligations is Paenitemini, published in 1966. This document comes right after the Second Vatican Council, which saw a great deal of change in practices across the Catholic Church. The document, in the introduction, states:
During the council, in fact, the Church, in an effort to arrive at a more profound meditation on the mystery of itself, examined its own nature in all its dimensions and scrutinized its human and divine, visible and invisible, temporal and eternal elements.
Later, it continues with:
Lastly, the Church has considered more attentively its role in the earthly city,(6) a that is to say, its mission of showing man the right way to use earthly goods and to collaborate in the "consecration of the world." But at the same time it has considered more attentively its task of prompting its sons to that salutary abstinence which will forearm them against the danger of allowing themselves to be delayed by the things of this world in their pilgrimage toward their home in heaven.
Then, dealing with the issue of penitence explicitly:
To recall and urge all the faithful to the observance of the divine precept of penitence, the Apostolic See intends to reorganize penitential discipline with practices more suited to our times. It is up to the bishops—gathered in their episcopal conferences—to establish the norms which, in their pastoral solicitude and prudence, and with the direct knowledge they have of local conditions, they consider the most opportune and efficacious.
These means [prayer—fasting—charity] were the same throughout the centuries, but in our time there are special reasons whereby, according to the demands of various localities, it is necessary to inculcate some special form of penitence in preference to others. Therefore, where economic well-being is greater, so much more will the witness of asceticism have to be given in order that the sons of the Church may not be involved in the spirit of the "world," and at the same time the witness of charity will have to be given to the brethren who suffer poverty and hunger beyond any barrier of nation or continent. On the other hand, in countries where the standard of living is lower, it will be more pleasing to God the Father and more useful to the members of the Body of Christ if Christians—while they seek in every way to promote better social justice—offer their suffering in prayer to the Lord in close union with the Cross of Christ.
Looking at the footnotes and references of the quote above, you find in the Sacrosantum concilium:
- During Lent penance should not be only internal and individual, but also external and social. The practice of penance should be fostered in ways that are possible in our own times and in different regions, and according to the circumstances of the faithful; it should be encouraged by the authorities mentioned in Art. 22.
Similarly, from Gaudium Et Spes:
Those Christians are to be praised and supported, therefore, who volunteer their services to help other men and nations. Indeed, it is the duty of the whole People of God, following the word and example of the bishops, to alleviate as far as they are able the sufferings of the modern age.
Importantly, the Pope does establish a minimum universal set of fasting rules (in Chapter III). But then gives more room to (i) local conditions and (ii) works of charity as another form of penitence.
In summary, Paenitemini states:
Therefore, the Church, while preserving—where it can be more readily observed—the custom (observed for many centuries with canonical norms) of practicing penitence also through abstinence from meat and fasting, intends to ratify with its prescriptions other forms of penitence as well, provided that it seems opportune to episcopal conferences to replace the observance of fast and abstinence with exercises of prayer and works of charity.
Can you go deeper than this? Well, that would involve some exegesis or speculation, perhaps with the help of news articles and interviews, for example in historical editions of L'Osservatore Romano (which seem not to be available online).
In conclusion, amid the spirit of change of the Second Vatican Council, fasting rules were relaxed (whilst keeping a common universal minimum) in order to give more freedom to local bishops to ordain particular rules, and also to make clear that works of charity are important in penitence. As the document states, penitence is a triad composed of "prayer - fasting - charity".