Assertion, n.
Etymology: [L. assertio, fr. asserere.]
1. The act of asserting, or that which is asserted; positive declaration or averment; affirmation; statement asserted; position advanced. There is a difference between assertion and demonstration. Macaulay.
2. Maintenance; vindication; as, the assertion of one's rights or prerogatives.
Shades of meaning
Fernald has no entry of its own for assertion; he lists it under assurance.
Where he writes about it:
To assert without proof is always to lay oneself open to the suspicion of having no proof to offer, and seems to arrogate too much to one's personal authority, and hence in such cases both the verb assert and its noun assertion have an unfavorable sense; we say a mere assertion, a bare assertion, his unsupported assertion; he asserted his innocence has less force than he affirmed or maintained his innocence. — from state