"mainly asserting" is correct and usable in written English.
You can use it when you want to imply that something is mostly or primarily focused on asserting an idea or opinion. For example: The article was mainly asserting that the government's plan for economic reform was flawed.
On this account, to say that there is a human right against torture is mainly to assert that there are strong reasons for believing that it is always wrong to engage in torture and that protections should be provided against its practice.
"Those who have argued that we are the natural owners of our rights and liberties," Graeber writes, "have been mainly interested in asserting that we should be free to give them away, or even to sell them".
A dissident group of plaintiffs, mainly from California, objected to the approach, asserting that the victims of the purported overcharging should benefit directly.
The proceedings mainly consisted of Representative Issa and others asserting that money spent on environmentally friendly fuels and jobs would be much better spent on "domestic carbon-based resources" — that is, dirtier fuels like oil, gas and coal.
But he said this year would be different, asserting that revenues were slightly higher than expected, mainly because businesses had been overpaying their taxes, following a practice of prepaying estimated taxes based on the previous year's profits.
It is in the lineup mainly so Nissan can assert that a new Altima costs as little as $16,889, including delivery.
Both sides were unanimous in asserting that the most demanding tasks must be undertaken in the public sector, mainly because the private sector is lacking adequate equipment.
He is asserting himself".
has been acquiring & asserting authority.
China asserting itself in Asia.
