Affirm has less of egotism than assert (as seen in the word self-assertion), coming nearer to aver. In legal usage, affirm has a general agreement with depose and testify; it differs from swear in not invoking the name of God.

J. C. Fernald, English Synonyms and Antonyms (1914)

Example sentences

swear When angry, count to four. When very angry, swear.
confirm I will neither confirm nor deny these allegations.
assert Taiwan can't assert its independence from China.
aver He had to aver that he was responsible for the mistake.

Popularity over time

Word	1850 → 2019	Trend
affirm		steady
swear		rising
confirm		rising
assert		steady
aver		falling

Use in printed books, per decade from 1850 to 2019.

By length

3 letters: say¹
4 letters: aver², avow²
5 letters: swear¹
6 letters: verify³, assert², attest², allege², ratify³
7 letters: support², protest², confirm², approve², declare², testify³, endorse², contend², profess²
8 letters: maintain², validate³
9 letters: establish³
10 letters: astipulate
11 letters: corroborate⁴
12 letters: substantiate⁴

The small number after each word is its number of syllables (aver² = 2 syllables).