It seems like almost every piece with an ornament has some argument as to how it is supposed to be played. For example, in my Alfred's edition of Fantaisie-impromptu, the footnote claims that the ornaments in the middle section should be played as trills starting on the upper note. However, most performers play it as a mordant. Also in Beethoven's Pathetique, some people play the mordents evenly and some play it as a triplet.
What is the cause of all this confusion around ornaments?
There are a couple things I would note. Most Classical music is pre-recording technology, so we don't have any recordings of how it would have been played at the time, which would likely be the way the composer would have intended it. Because of this, we have to rely on the notation alone. The older the piece of music, the less standardized the notation practices of the time were. There were also some different standards for different regions, as travel wasn't as common, and long-distance communication was strictly letters.
You also have to consider that different editors can have an impact on what is being played. Sometimes they add or remove things from certain pieces, presumably in an attempt to live up to the composer's intentions. They are essentially imposing their interpretation of the music onto the score, so you're basically looking at a score that could be "wrong" sometimes. People who are familiar with the different publications of the same pieces will point out these differences and allow a more open debate about the "correct" interpretation.
The older the music, the less likely there will be agreement on how it should be interpreted, especially if it was "lost" for a period of time. Bach's music was famously rediscovered by Mendelssohn. It had been around 100 years since Bach's death before his music was rediscovered, so it was well removed from the traditions of baroque music, leaving a lot of room for interpretation. There are lots of people who dive into music history/musicology and attempt to get a better understanding of different periods, so we tend to see several different sorts of knowledge pools. Some people have a long teaching lineage, so they were taught/are teaching based on a tradition, potentially as far back as the time period of the music they're playing. You could argue that those people would have the best insights/interpretations; however, you do have to consider the Telephone Game effect taking place here. The historians and musiciologists would derive their interpretations from research, potentially avoiding the Telephone Game phenomenon, but they're also forced to figure it all out from the writings they can find.
TL;DR: it's old music, we don't always have great references, and sometimes people have imposed their interpretations onto the music we read.
The confusion is caused by at least two reasons: much of performance practice was not notated precisely, and performance practice was not uniform.
If you look at something like JS Bach's well know ornament table from the Klavierbüchlein für Wilhelm Friedemann Bach...
...it would seem the matter is simply to execute what is on the chart.
But, if you look at treatises like...
...you will see the extent to which players were expected to extemporize. Players were expected to not only ornament but improvise. They were expected to know musical conventions and show good judgment. Scores were written with an expectation for the player to interpret. (To varying degrees and changing over time.) A player's musical taste was the measure, not merely executing an ornament as defined on a chart.
..the footnote claims that the ornaments in the middle section should be played as trills starting on the upper note. However, most performers play it as a mordant.
Whatever the case is there should be good reasons either technical or artistic for one choice or another.
If someone disputes another's choices and allows no room for alternatives, it can approach factionalism or dogma.
Your questions suggests or implies that the art of art should always be the same in all times and everywhere but it’s just that the art of art has been changing and still changes everywhere and every time. So each artist has his own art to play any piece of art and some write it down like Quantz and C.P.E. Bach and now you can play a piece in the style of the art and kind of Chopin or Glenn Gold or Miles Davies or in the style and art of your own art, if others will follow you will be an artist yourself. There are always artists who want to make doctrine which art is the only perfect correct and true art to play something and that’s the way and art they are playing! We have the same appearance in religions and politics, sports and fashion. Here we call them leaders, Führer or gurus or trendsetters.
