We generally think of holiness in this sense as describing human beings who live by the laws of kashrut.
An anthropological view which applies “holy” to the animals themselves is provided by Mary Douglas in a book called “Purity and Danger”, published in 1956.
She says that “to be holy is to be whole” and those creatures which are named as kosher are a higher, more perfect form of their species. The pig lacks this quality and is therefore not holy and not kosher.
It’s an interesting theory, but for Judaism the acceptability or otherwise of a given creature is not dependent on anthropological theory but on Divine wisdom.