1
general::
Listen to someone's discourse until the end, allow someone to speak fully, as in Please hear me out before you jump to any conclusions. [First half of 1600s]
American Heritage Idioms
2
general::
Phrase(s): hear someone out
1. Lit. to hear all of what someone has to say. (Fixed order.) • Please hear me out. I have more to say. • Hear out the witness. Don’t jump to conclusions. 2. Fig. to hear someone’s side of the story. (Fixed order.) • Let him talk! Hear him out! Listen to his side! • We have to hear everyone out in this matter.
McGrawhill's American Idioms And Phrasal Verbs