tolkiens legendarium - Why does Saruman identify himself as a human?

Saruman, just before he imprisons Gandalf, says the following:

The Elder Days are gone. The Middle Days are passing. The Younger Days are beginning. The time of the Elves is over, but our time is at hand: the world of Men, which we must rule.

Saruman and Gandalf are Maiar and they are speaking alone so why would he say this?

The answers to this question say that what we are reading is the story as told by Hobbits who didn't know the true nature of Istari. Howerver, this particular passage seems to come from Gandalf's precise account of his conversation with Saruman. It seems that Saruman is trying to make a very specific argument to persuade Gandalf to his plan which doesn't seem to make much sense since neither of them is a human.

I'm not necessarily looking for an in-universe explanation. So I am also interested in knowing whether at the time of writing these words Tolkien has already decided the precise nature of the Wizards.

Answer

This need not necessarily be read as the Istari self-identifying as human. A valid interpretation might be the following paraphrase:

Our time is at hand and we must rule the world of Men.

By that interpretation they can obviously still self-identify as Maiar but nonetheless rule the world of Men.

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Despite that, the Istari material in Unfinished Tales confirms that their physical form in Middle-earth was human:

For with the consent of Eru they sent members of their own high order, but clad in bodies as of Men, real and not feigned, but subject to the fears and pains and weariness of earth, able to hunger and thirst and be slain; though because of their noble spirits they did not die, and aged only by the cares and labours of many long years.

So therefore it is also valid to interpret Saruman's statement as self-identifying as human, because physically the Istari were Men.

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Part of Saruman's Fall was that he had lost contact with his spiritual purpose and become focussed on the physical; as Treebeard puts it in the Two Towers:

He has a mind of metal and wheels; and he does not care for growing things, except as far as they serve him for the moment.

Also Merry's words:

I think he has not much grit, not much plain courage alone in a tight place without a lot of slaves and machines and things, if you know what I mean.

It's in keeping with this that Saruman begins to self-identify with his physical form rather than his spiritual being, although that conclusion is conjectural and - as my first point establishes - is not even necessary to explain his words.