Assertion vs Counterassert - What's the difference?

As a noun assertion

is the act of asserting, or that which is asserted; positive declaration or averment; affirmation; statement asserted; position advanced.

to assert in opposition to a previous assertion.

(en noun)

The act of asserting, or that which is asserted; positive declaration or averment; affirmation; statement asserted; position advanced.

Maintenance; vindication; as, the assertion of one's rights or prerogatives.

(computing) A statement in a program asserting a condition expected to be true at a particular point, used in debugging.

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(en verb)

To assert in opposition to a previous assertion

*{{quote-book, 1974, Colin Fletcher, The New Complete Walker, page=36 citation

, passage=Roughouts, some pundits assert, are therefore superior. Other pundits counterassert , fiercely.}}