First of all, let us eliminate a misconception. St. Paul is not speaking of the Mass in this passage of Scripture. He is speaking of an agape meal and not the Mass. He admits as much in saying ”it is not now to eat the Lord's supper.” Thus it is not the remembrance of the the Lord’s Last Supper!
St. Paul in reality is describing the meal known as Agape.
The celebration of funeral feasts in honour of the dead dates back almost to the beginnings of the worship of the departed - that is, to the very earliest times. The dead, in the region beyond the tomb, were thought to derive both pleasure and advantage from these offerings. The same conviction explains the existence of funeral furniture for the use of the dead. Arms, vessels, and clothes, as things not subject to decay, did not need to be renewed, but food did; hence feasts at stated seasons. But the body of the departed gained no relief from offerings made to his shade unless these were accompanied by the obligatory rites. Yet the funeral feast was not merely a commemoration; it was a true communion, and the food brought by the guests was really meant for the use of the departed. The milk and wine were poured out on the earth around the tomb, while the solid food has passed in to the corpse through a hole in the tomb.
The use of the funeral feast was almost universal in the Græco-Roman world. Many ancient authors may be cited as witnesses to the practice in classical lands. Among the Jews, averse by taste and reason to all foreign customs, we find what amounts to a funeral banquet, if not the rite itself; the Jewish colonies of the Dispersion, less impervious to surrounding influences, adopted the practice of fraternal banquets. If we study the texts relative to the Supper, the last solemn meal taken by Our Lord with His disciples, we shall find that it was the Passover Supper, with the changes wrought by time on the primitive ritual, since it took place in the evening, and the guests reclined at the table. As the liturgical meal draws to a close, the Host introduces a new rite, and bids those present repeat it when He shall have ceased to be with them. This done, they sing the customary hymn and withdraw. Such is the meal that Our Lord would have renewed, but it is plain that He did not command the repetition of the Passover Supper during the year, since it could have no meaning except on the Feast itself. Now the first chapters of the Acts of the Apostles state that the repast of the Breaking of Bread took place very often, perhaps daily. That which was repeated was, therefore, not the liturgical feast of the Jewish ritual, but the event introduced by Our Lord into this feast when, after the drinking of the fourth cup, He instituted the Breaking of Bread, the Eucharist. To what degree this new rite, repeated by the faithful, departed from the rite and formulæ of the Passover Supper, we have no means, at the present time, of determining. It is probable, however, that, in repeating the Eucharist, it was deemed fit to preserve certain portions of the Passover Supper, as much out of respect for what had taken place in the Cœnaculum as from the impossibility of breaking roughly with the Jewish Passover rite, so intimately linked by the circumstances with the Eucharistic one.
This, at its origin, is clearly marked as funerary in its intention, a fact attested by the most ancient testimonies that have come down to us. Our Lord, in instituting the Eucharist, used these words: "As often as you shall eat this Bread and drink this chalice, you shall show forth the Lord's Death". Nothing could be clearer. Our Lord chose the means generally used in His time, namely: the funeral banquet, to bind together those who remained faithful to the memory of Him who had gone. We must, however, be on our guard against associating the thought of sadness with the Eucharistic Supper, regarded in this light. If the memory of the Master's Passion made the commemoration of these last hours in any measure sad, the glorious thought of the Resurrection gave this meeting of the brethren its joyous aspect. The Christian assembly was held in the evening, and was continued far into the night. The supper, preaching, common prayer, the breaking of the bread, took up several hours; the meeting began on Saturday and ended on Sunday, thus passing from the commemoration of the sad hours to that of the triumphant moment of the Resurrection and the Eucharistic feast in very truth "showed forth the Lord's Death", as it will until He come". Our Lord's command was understood and obeyed.
Certain texts refer to the meetings of the faithful in early times. Two, from the Epistle of St. Paul to the Corinthians (1 Corinthians 11:18, 20-22, 33, 34), allow us to draw the following conclusions: The brethren were at liberty to eat before going to the meeting; all present must be in a fit condition to celebrate the Supper of the Lord, though they must not eat of the funeral supper until all were present. We know, from two texts of the first century, that these meetings did not long remain within becoming bounds. The agape, as we shall see, was destined, during the few centuries that it lasted, to fall, from time to time, into abuses. The faithful, united in bodies, guilds, corporations or "collegia", admitted coarse, intemperate men among them, who degraded the character of the assemblies. These Christian "collegia" seem to have differed but little from those of the pagans, in respect, at all events, of the obligations imposed by the rules of incorporation. There is no evidence available to show that the collegia from the first undertook the burial of deceased members; but it seems probable that they did so at an early period. The establishment of such colleges gave the Christians an opportunity of meeting in much the same way as the pagans did - subject always to the many obstacles which the law imposed. Little feasts were held, to which each of the guests contributed his share, and the supper with which the meeting ended might very well be allowed by the authorities as a funerary one. In reality, however, for all faithful worthy of the name, it was a liturgical assembly. The texts, which it would take too long to quote, do not allow us to assert that all these meetings ended with a celebration of the Eucharist. In such matters sweeping generalizations should be avoided. At the outset it must be stated that no text affirms that the funeral supper of the Christian colleges must always and everywhere be identified with the agape, nor does any text tell us that the agape was always and everywhere connected with the celebration of the Eucharist. But subject to these reservations, we may gather that under certain circumstances the agape and the Eucharist appear to form parts of a single liturgical function. The meal, as understood by the Christians, was a real supper, which followed the Communion; and an important monument, a fresco of the second century preserved in the cemetery of St. Priscilla, at Rome, shows us a company of the faithful supping and communicating. The guests recline on a couch which serves as a seat, but, if they are in the attitude of those who are at supper, the meal appears as finished. They have reached the moment of the Eucharistic communion, symbolized in the fresco by the mystical fish and the chalice.
Tertullian has described at length (Apolog., vii-ix) these Christian suppers, the mystery of which puzzled the Pagans, and has given a detailed account of the agape, which had been the subject of so much calumny; an account which affords us an insight into the ritual of the agape in Africa in the second century. - Agape (Catholic Encyclopaedia)