Why is the hired servant not allowed to eat the holy thing in Leviticus 22:10-11?
What was the major difference between the hired servant and slave that could have warranted that a slave partake of the holy thing ahead of a hired servant?
A hired servant was usually not an Israelite but someone from the surrounding nations. The article Hired Laborer, or hired servant in KJV, in Insight on the Scriptures says the following:
Evidently in Israel many of the hired laborers were uncircumcised, for the Law prescribed that they not partake of the Passover, although circumcised slaves could do so, being viewed as members of an Israelite family. Likewise, while the hired laborers of a priest could not eat of the holy things, no such prohibition rested on circumcised slaves, as these were also actually members of the priest’s household.—Ex 12:43-45; Le 22:10, 11.
So, a slave was circumcised and therefore considered "clean" under the Mosaic Law. Hired workers were not circumcised and therefore "unclean" and could not partake of the Passover meal. If they were unclean for the Passover then they would also be unclean to eat the holy foods given to the priests.