On shabbat we don't wear tefillin because shabbat is an אות. However yom tov is not referred to as an אות. So why don't we wear tefillin on yom tov?
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The Rambam (Hil. Tefilin 4:10) disagrees with you. He says:
The Rambam says clearly that Yom Tov is an אות and therefor does not warrant putting on Tefillin.
The Rambam's source is a Gemara (Menachot 36):
The question now becomes: How is Yom Tov an אות?
The Aruch Hashulchan in Hil. Tefilin 31:3 answers this in 2 ways:
Additionally, Pesach Mitzrayim is refered to in the Torah as an ot, and as all the yamim tovim are connected to the Exodus, there's a sort of transitive operation by which the others can be considered otot as well.