What evidence have you seen for this (it does not match what I have read, but I am interested)? The Greek word (pardon me, but I think what we know of the original text matters) for the garment is "chitona" and then "chiton", which is normally translated as 'coat'.
I would guess that Jesus wore more or less:
a linen undershirt, the "haluk";
a tunic over the haluk;
a linen girdle around the waist;
sandals made of untanned leather (perhaps leather boots in the winter);
and an upper garment, probably made of white wool, with a blue thread in the garment and tassels at the corners, which may have been a Talit or similar but probably would not have been referred to as a 'chiton'.
He may, perhaps, have worn a head covering, with a woolen circlet to hold it in place, particularly in the summer;
or a thick woolen "himation" as a coat for warmth in the winter.
As I understand the words and First Century clothing, the tunic or the himation are the most likely items to have been referred to as a 'chiton'. Both practical items would have been valued by Roman soldiers far more than the more symbolic Talit (prayer shawl) would.
In order to be our savior, Yeshua had to be completely Torah observant, thus he wore the Talit that all men were required to wear.
The Talit is the garment with the blue thread in the corner tassels that the woman touched
You cannot go by the Greek because it was translated from the original Hebrew writings by persons that lacked understanding of Torah and Hebrew culture.
The Greek texts are heavily peppered with cultural faux pas that show clearly that this is so.
This is not something we can check out though, except for Matthew’s gospel where 28 lines of copies of the original Hebrew are available,and they differ considerably with the received Greek texts.
All it means is that you just can’t rest on what a word traditionally meant in Greek. You have to compare it through finding the same word in the LXX, which was translated by Hebrew scribes, and relating that word to the same line in the Tanakh to see what the Hebrew really is.
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Any cloth represented a huge investment of labor. . . as such was worth a lot of money. Cloth in the pre-industrial age was extremely valuable and in fact, often represented a large portion of the value of many estates. You may recall that Scrooge in a Christmas Carol was watching the people going through his Household LINENS, a very valuable portion of his estate. . . and a big consideration in one's last will and testament. Especially Flaxen Linens over cotton goods, as Linen could last generations.
This is why a coat or garment made without a seam would be particularly valuable. First it had to be extremely fine, being woven or knitted, crocheted as one piece. Secondly, had to be the work of a long time, involving weeks of work to grow the linen, spin and ret the yarn, then weave the garment on a special loom, most likely a special rig, by a skilled artisan. It was not something that was made from square pieces just assembled and sewn into one pieces from several.
It is also why grave clothes and Shrouds are very rare and usually were as small as possible and usually made of used sails, if they were used at all.