The connection to Hashem’s holiness
The possuk continues with יכֶםוקלא ה'כִּי קָדוֹשׁ אֲנִּי – for I, Hashem your G-d, am holy. How is this a reason for the commandment to be holy? A human is not commanded to imitate Hashem, that would be impossible. Why is the Divine trait of holiness something that must be imitated, and how is that obvious? It is possible the Torah merely means to tell us that Hashem wished that we imitate Him in this way, but that does not explain why the Torah wrote it in the language of a reason for the Mitzvah.
The Chachamim seemingly noticed this question, and they explain, in Toras Cohanim, the meaning of the possuk. They write that a person who sanctifies himself in this world is considered as though the person has sanctified Hashem.
Now, the meaning of the possuk is that we should be holy, because through that, Hashem is also holy. The opposite is also true. The Medrash says that if they don’t sanctify themselves, Hashem’s holiness is compromised.
This is another meaning of the double expression. If Klal Yisroel sanctifies themselves, they are so great that they increase holiness on high. But if they don’t, the problem is so great that Divine holiness is also compromised.
