Disbelieve often suggests a strong emotional resistance to accepting something as true. Even after apologizing, I could see she disbelieved my sincerity.
Pro Tip 2/3
Associated Negativity
'Disbelieve' may imply a negative attitude towards the speaker or the information presented. The jury was instructed to disbelieve the witness due to his inconsistent testimony.
Pro Tip 3/3
Contextual Use
Use 'disbelieve' when expressing doubt about commonly held facts or well-known stories. You may disbelieve in ghosts, but I've seen one with my own eyes.