The phrase "assert instead" is correct and usable in written English.
You can use it when suggesting that someone should state or declare something in place of another option or idea.
Example: "If you disagree with the proposal, you should assert instead your own viewpoint clearly."
Alternatives: "state instead" or "declare instead".
They assert, instead, that he makes a full-time living as an expert witness.
These therapists assert, instead, that gender confusion is a result of childhood trauma and that sexual orientation can be reshaped.
She will assert instead that severe recessions can provide dangerous incentives for large and dominating companies to engage in predatory behavior that harms consumers and weakens competition.
But there does not seem to be any reason the combinatorialist cannot simply deny the primitiveness of the modality here and assert instead that it is just a fact about recombination that a and S do not co-exist in any combinatorial possible world, that a world in which a exists is not one where S does and that this non-modal fact is the truthmaker for the modal proposition above.
The president asserted instead that "we've blunted the Taliban's momentum".
This account asserts, instead, that they were made by an Icelandic craftswoman mentioned in the sagas.
He asserted instead that leftist Basque radicals had themselves set fire to it.
Congress should abandon its impeachment investigation, Specter asserted; instead, Clinton should face a possible criminal prosecution after his term ended.
The Peak was magnificently oblivious of such uncertainty, asserting instead the liberating power of inventing new forms and spaces.
Elizabeth Cobbs Hoffman asserts instead that, because of its unusual federal structure, America has performed the role of umpire since 1776, compelling adherence to rules that gradually earned collective approval.
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.
