Zapewniam cię, że nie jest to moim zamiarem.

English Translation

But I assure you, that is not my intention.

why is the instrumental case being used here? Even though we are directly referring to “to” here. I would assume because of that, the nominative would be used.

In this sentence, “to” is used as a particle (meaning “this”, or “this thing”), and not as a conjunction (meaning “is”).

In the phrase “nie jest to moim zamiarem”, “to” is the subject, and the instrumental case is used here because it’s required by the verb “jest”.