Rabbi Yair Hoffman quotes the gemara Chullin 105a which gives the original halacha.
Waiting 5 and 1/2 Hours Versus 6 Hours – a Halachic Analysis
“Rav Chisda said: One who eats meat may not eat cheese, [one who eats]
cheese, may eat meat…
Mar Ukvah said: Regarding this, I am like
vinegar, the son of wine. My father, if he would consume meat today,
would wait until tomorrow to eat cheese. I, however, will not consume
them during the same meal, but at another meal I will eat cheese.”
The Rif writes that by virtue of the fact that Mar Ukvah referred to
himself as “vinegar the son of wine” – no authority permits a waiting
period of less than six – from the morning meal to the evening meal.
The Baalei HaTosfos disagree and understand the notion of another meal
to refer even to a case where a second meal was started right away.
[This is also the position of the Mordechai, the HaGaos Ashri, the
Hagaos Maimonius and the Raavya.]
Rabbi Hoffman then analyzes the meaning of this. It would appear that the Baalei Tosfos would say that the wait of six hours is definitely a minhag, since the Ashkenazic community took on the longer wait. The fact that the Dutch and German communities wait different amounts, seems to imply that the interval of "next meal" was established by community minhag.
This is not to suggest that other customs are, heaven forbid,
incorrect. Customs among observant Jews range the gamut from one hour
(Dutch Jews) to three hours (German and British Jews) to five hours to
five and half hours. But a number of questions do arise: What should
these students who wait six hours be doing? Should the students undo
their family tradition and adopt that of their Yeshiva? Also from
where did the customs of 6 hours and 5 and ½ arise?
Rabbi Hoffman discusses the difference between 5.5 (miktzah kekulo) and 6 hours which again seems to imply that the gezeirah of waiting until the "next meal" as a set interval appears to be a community minhag as far as what that interval might be. Note that he specifically does this because a problem has arisen in some yeshivos which use the 5.5 hour minhag while the family minhag of many students is to wait the full six hours.
This means that Rabbi Hoffman regards the specific time used for the gezeira of a set interval as a minhag. Thus, מנהג אבותינו תורה היא would be the reason for the psak that he cites.
The Poskim replied that, notwithstanding all of the combined factors
above to be lenient, it was indeed a problem and that these students
should not be forced by the Yeshivos to negate their own family
practices. This was the ruling of a number of American Poskim as well
as Rav Vosner zt”l in Eretz Yisroel.
The Chof-K points out Waiting Six Hours between Meat and Dairy that this is a gzeirah miderabbonon (Shulchan Aruch 89:1)
The chachumim made a gezeira that even if the meat and milk
are not cooked together, you may not eat milk after eating
any type of meat or chicken before waiting six hours.