Why do priests celebrate Mass versus populum (toward the congregation) at most Masses in the Ordinary Form? Why do priests celebrate Mass versus populum (toward the congregation) and at most Masses in the Ordinary Form?
Why do priests celebrate Mass versus populum (toward the congregation) at most Masses in the Ordinary Form?
Before getting into the crux of this question, let us see what the origin’s of this tradition might be. We can not truly understand this issue unless we can understand its’ origin.

Early evidence of Christian praying towards the east
Tertullian (c. 160 – c. 220) says that, because Christians faced towards the east at prayer, some non-Christians thought they worshipped the sun.
Clement of Alexandria ( c. 150 – c. 215) says: &quot;Since the dawn is an image of the day of birth, and from that point the light which has shone forth at first from the darkness increases, there has also dawned on those involved in darkness a day of the knowledge of truth. In correspondence with the manner of the sun's rising, prayers are made looking towards the sunrise in the east.&quot;
Origen (c. 185 – 253) says: &quot;The fact that [...] of all the quarters of the heavens, the east is the only direction we turn to when we pour out prayer, the reasons for this, I think, are not easily discovered by anyone.&quot;
Later on, Fathers of the Church such as John of Damascus advanced mystical reasons for the custom.
Origin of the practice
The primitive Church had no knowledge of the origin of the practice. Origen says: &quot;The reasons for this, I think, are not easily discovered by anyone.&quot; Although the general custom among Jews was to pray towards the temple in Jerusalem, Clement of Alexandria, Origen's older contemporary, says that the custom of praying eastward was general even among non-Christians: &quot;In correspondence with the manner of the sun's rising, prayers are made looking towards the sunrise in the east. Whence also the most ancient temples looked towards the west, that people might be taught to turn to the east when facing the images.&quot;
In 1971, Georg Kretschmar proposed a connection between the Christian custom of praying towards the east and a practice of the earliest Christians in Jerusalem of praying towards the Mount of Olives, to the east of the city, which they saw as the locus of key eschatological events and especially of the awaited Second Coming of Christ. In his view, the localization of the Second Coming on the Mount of Olives was abandoned after the destruction of Jerusalem in AD 70, but the eastward direction of Christian prayer was retained and became general. Stefan Heid rejects his theory, but Lang holds that it is not without reasons to support it.
Martin Wallraff held that at the time of the formation of Christianity Jews prayed as commonly towards the east as towards the Jerusalem temple, but Lang considers that the eastward posture was rare among Jews. It was the practice, Paul F. Bradshaw says, of the Jewish sects of the Essenes and the Therapeutae, for whom &quot;the eastward prayer had acquired an eschatological dimension, the 'fine bright day' for which the Therapeutae prayed being apparently the messianic age and the Essene prayer towards the sun 'as though beseeching him to rise' being a petition for the coming of the priestly Messiah.&quot; - Ad orientem (Wikipedia)

Celebrating the Mass facing the people is a centuries-old practice, although the vast majority historically said the Mass facing east.

After the Council, detailed directions for the celebration of the revised form of Mass were drawn up, including an instruction that the priest should celebrate Mass facing the people.
No, I am not referring to the Second Vatican Council or Inter Oecumenici or the GIRM. This was the Council of Trent (1545 – 1563), and the relevant documents were prepared under the leadership of St Charles Borromeo, the archbishop of Milan. He had not attended the Council, but he became a major implementer of the disciplinary reforms that the Council promulgated. Many of these were about removing superstitious ceremonial from the Mass; others spoke directly to the conduct of bishops and priests. The former were to avoid silken vestments, expensive furs, rings other than the episcopal ring; the latter were to exhibit restraint in their clothing and personal furnishings. Both were expected to exercise simplicity and moderation in every aspect of their lives. The splendor of faith was to be preferred to ornate display. You might say that St Charles anticipated the call for ‘noble simplicity’ of a later Council.
He also wrote extensively about the construction and furnishings of churches, in a document published in 1577, Instructiones fabricae et supellectilis ecclesiasticae. Chapter 10 speaks about the principal chapel of any church:

The site of this chapel must be chosen at the head of the church, in a prominent place and on an axis with the main entrance. The back part should face east, even if there are houses behind it. It must not face to the east of the summer solstice, but towards that of the equinox.


If this is not possible, the Bishop can decide and permit that it be built facing another direction, but in this case care must be taken at least that if possible it does not face north, but south. In any case the chapel in which the priest celebrates Mass from the high altar facing the people, in accordance with the rites of the Church, must face west.

In other words, orientem means simply “east”. When the priest celebrates at the main altar, facing the people, “in accordance with the rites of the Church”, he is to face east.
The historian John O’Malley asserts that Borromeo sought to standardize and promote a number of liturgical practices. Some were broadly adopted – for instance, placing the tabernacle in the center of the main altar. Others, which Borromeo had advocated, were not – O’Malley cites celebration with the priest facing the people as an example.
Uwe Lang speaks about Borromeo in his book about the orientation of liturgical prayer:

… the archbishop of Milan says that the capella major must be oriented, with the main altar facing east.  Where this is impossible, it can be directed towards another cardinal point (except north) but preferable toward the west, ‘as, in accordance with the rite of the Church (pro ritu Ecclesiae) the sacrifice of the Mass is celebrated at the main altar by the priest with his face turned towards the people.’

But Lang airily dismisses this as an exception:

Borromeo must have had in mind those Roman basilicas with a westward apse and an eastward entrance, where Mass was celebrated facing the people; this practice was no doubt familiar to him. Still, for Borromeo, the eastward direction was the paramount principle for liturgy and church architecture.

Celebration facing the people did not become normative, as (per O’Malley), St Charles Borromeo had wished it would. But this bit of history seems to give the lie to claims that celebration facing the people was a fabrication of the 20th century liturgical movement, or of misinterpretation of the Second Vatican Council. - Celebration facing the people: a centuries-old practice

While the current edition of the Roman Missal assumes that Masses are to be celebrated “ad orientem,” it is also permitted to celebrate “facing the people”. So, both ways are allowed.
No Vatican II document said that priests must face &quot;toward the people&quot; (versus populum). In fact, all Masses today can be celebrated ad orientem (&quot;toward the east,&quot; the same direction the people face, which is toward the tabernacle). However, modern church architecture has made all but impossible to do so in many regions.
In many older churches, especially in Europe there are altars that make it an obligation for a priest to say the New Mass &quot;ad orientem&quot;, facing east. Visit St Peter's Basilica at the Vatican for example.
There is no one correct answer as to why so many priests celebrate Mass facing the people. But some hints do exist.

The Mass versus populum is completely liturgically permitted by Rome.
Sadly, almost every church built or renovated since 1965 has significant design impediments to celebrating the Mass ad orientem. Because of confusion about what exactly the Second Vatican Council’s reform of the Mass required of sacred architecture, the traditional design of a church was radically altered in such a way that a return to the traditional posture of the priest facing liturgical East is difficult, if not impossible, in many churches. (Source)
Non-traditional Catholic seminaries need to teach their students the significance of saying the Mass “ad orientem”. Traditional gestures within the Mass need to be instilled into seminarians studying for the priesthood. Sadly this not being done in any great degree.
The faithful need to also to be taught the significance of the gesture of saying the Mass “ad orientem” so that the true symbolism of this gesture would be more easily accepted.
Some (with just cause) have reasoned that Jesus had the Apostles more or less in a circle or a U shape at the Last Supper when he instituted the Mass. Impossible to say whether or not Jesus faced east
(”ad orientem”). Jesus definitely faced his Apostles at the institution of the first mass. Source
Did Jesus have His Last Supper standing?

It should be noted that at Papal High Masses within the Roman Basilica of St. Peter, in either the Ordinary Form of the Mass or the Extraordinary Form of the Mass are both facing the people and the Sovereign Pontiff is still facing east (ad orientem).
As far as the Tridentine Mass goes the YouTube video Mass In Vatican With Pope Pius XII bears this fact out.
Part of this reason is the the actual basilica faces east.

Rome tourist attractions map
The traditional liturgical posture is to face East. That is the direction of the dawn, the new light and thus facing the direction of the returning Christ.
Most churches were built so that that the direction of worship literally faced East (traditional synogogues are also built in this manner).
However, St. Peters was not be build that way. Constantine literally had to carve into the side of Vatican Hill to get enough room to build the original basilica so that the altar was over the burial place of St. Peter. For these reasons, both Latin Rites share a common tread with the Supreme Pontiff facing east and facing the people at the same time.
A floor plan of St. Peter’s Basilica makes this unique unity between the the Roman Rite more understandable.