The phrase "assert rather than" is correct and usable in written English.
You can use it when you want to emphasize the act of stating something confidently instead of choosing an alternative action or approach.
Example: "In this debate, I choose to assert rather than remain silent on the issue."
Alternatives: "state instead of" or "declare rather than".
Mr Piketty asserts rather than explains why tempering wealth concentration should be the priority (as opposed to, say, boosting growth).
Even its stated premise, that the SDNY is the crown jewel of America's lower federal courts, is asserted rather than demonstrated: the author fails to compare its historical importance or quality of jurisprudence with those of any other district, and dedicates half a chapter to lampooning its least distinguished judges.
Samuel Alexander asserted, rather than argued, that mentality strongly emerged from space-time, and then that at some future time there will emerge a new and at present hardly imaginable level which he called 'deity' (Alexander 1927).
He ignored or opposed systematic philosophy, had little faith in rationalism, asserted rather than argued many of his main ideas, presented others in metaphors, was preoccupied with immediate and personal experience, and brooded over such questions as the meaning of life in the face of death.
As Tarek's father, Dr. Mahmoud Loubani asserts, rather than punish them, "If the Egyptian authorities...know about their mission, they should reward them and be proud of them".
Many high-profile witnesses in criminal trials repeatedly assert forgetfulness, rather than risk making a mistake by being too precise on the stand.
Since the start of the trial, the US Patent Office has upheld one of the patents that Google had contested; that means that Oracle will be able to assert three rather than two patents during the second part of the case.
