The phrase "asserting it" is correct and usable in written English.
You can use it when you want to indicate that someone is stating or declaring something confidently or firmly.
Example: "In her speech, she was asserting it as a fact that climate change is a pressing issue."
Alternatives: "stating it" or "declaring it."
In his masterful essay The Storyteller, Walter Benjamin draws a distinction between storyteller and novelist, asserting, "it is half the art of storytelling to keep a story from explanation as one reproduces it".
You have to credit the south-west; it has done quite the PR job on clotted cream, asserting it (with its PDO status) as the natural choice in a cream tea, despite it having nothing to recommend it.
Last October, the attorneys general of New York, New Jersey and Montana threatened to sue FedEx Ground, asserting it had misclassified its drivers.
The US establishes its power by asserting it.
It may be asked whether a statement of the world's unity is a precondition for asserting its identity with God, or a consequence of asserting it?
Iran insists its purposes are purely civilian, asserting it needs enriched uranium to make medical isotopes.
In agreement was @tobyjenn, asserting it had "technical nous above and beyond its challengers, with superb cinematography and an absolutely glorious soundtrack.
The pro-Diem Times of Vietnam published an article on 9 June which claimed that Cambodian monks had been encouraging the Buddhist crisis, asserting it was part of a Cambodian plot to extend its neutralist foreign policy into South Vietnam.
The National Rifle Association, along with its allies in Congress, has long opposed the treaty, asserting it would impinge on the constitutional right to bear arms, an argument that treaty proponents dispute.
This October the EU also ordered Amazon to pay $295M in back taxes, asserting it had been given illegal tax benefits in Luxembourg where its corporate HQ is based.
While the Trump Administration never stopped asserting it would, the White House never provided any research to back up its claim.
