From Latin 'clamare' (to call out), from PIE *kelh1- (to shout) — every claim is etymologically a public shout.
To assert that something is true or is the case; to demand as one's due or property.
From Middle English 'claimen,' borrowed from Old French 'claimer, clamer' (to call, name, claim, demand), from Latin 'clāmāre' (to call out, shout, proclaim), from PIE *kelh₁- (to shout, call). The original sense was deeply vocal: to claim something was to shout one's right to it publicly, to call out in the hearing of witnesses that something belonged to you. The legal sense of asserting a right and
The words 'claim,' 'exclaim,' 'proclaim,' 'acclaim,' and 'clamor' all come from Latin 'clāmāre' (to shout). An 'exclamation' is literally a 'shouting out,' a 'proclamation' is a 'shouting forth,' and 'acclaim' is 'shouting toward' someone in approval. Every claim you make is, etymologically, a public shout.