The phrase "asserts instead" is correct and usable in written English.
It can be used when you want to indicate that something is being stated or claimed in place of something else.
Example: "The author asserts instead that the solution lies in a more collaborative approach."
Alternatives: "claims instead" or "states instead".
This account asserts, instead, that they were made by an Icelandic craftswoman mentioned in the sagas.
Mr. Berezovsky never owned a stake in Sibneft, he asserts; instead, his role in that and other deals was to provide "krysha," literally "roof," or protection.
The two are the same except the former is silent about what duties one may owe to others and asserts instead that one has no enforceable duties to aid others, except those that arise from voluntary agreement and prior wrongdoing.
What it asserts instead is that every member of the reference class possesses a certain disposition, which in the case of statistical laws is of probabilistic strength and in the case of universal laws of universal strength.
As contemporary philosophers, we might wonder whether Berkeley has anything to say to a materialist who denies this representationalist premise and asserts instead that we ordinarily directly/immediately perceive material objects themselves.
He asserts instead that this need arises "from an objective determining ground of the will" (5:143n) and, at least as argued in the Critique of Practical Reason, the Highest Good is an object of faith for us, because it is "an a priori necessary object of our will and inseparably bound up with the moral law" (5:114).
They assert, instead, that he makes a full-time living as an expert witness.
The president asserted instead that "we've blunted the Taliban's momentum".
Congress should abandon its impeachment investigation, Specter asserted; instead, Clinton should face a possible criminal prosecution after his term ended.
These therapists assert, instead, that gender confusion is a result of childhood trauma and that sexual orientation can be reshaped.
The Peak was magnificently oblivious of such uncertainty, asserting instead the liberating power of inventing new forms and spaces.
