disobedient: describing a person who has been addressed, will not be won over, and so refuses to comply
This is the adjective of a small family built on the ordinary Greek verb for persuading someone and winning them over, with a prefix that cancels it. The verb of the family (ἀπειθέω) names the act of refusing, the noun (ἀπείθεια) names the refusal itself, and this word describes the person. So it is a label for character rather than for one bad moment: someone has heard, and will not be moved.
Because it describes people, the New Testament mostly uses it as a tag in a list. Paul drops it into two catalogues of what human life looks like once it turns from God, where the specific charge is being ungovernable toward one's own parents (Romans 1:30 and 2 Timothy 3:2). Titus uses it of people whose daily lives contradict what they claim about God, and then of himself and his readers before they were changed. Luke uses it as a bare name for a whole group, "the disobedient," the very people John the Baptist is sent to turn.
The one place the thing refused is actually named is Paul standing before Agrippa, saying he was not disobedient to the heavenly vision (Acts 26:19). That negative is a good test of the word: what he did not do was refuse to be persuaded by something God had shown him. The word never says a person failed to understand or was honestly unsure. It says they were addressed, and said no.
One difference from the rest of the family is worth noticing. The verb is so close to unbelief that English Bibles sometimes render it "do not believe," but this adjective is never treated that way, and it is never set opposite the word for trusting. For the missing trust itself the New Testament reaches instead for a different adjective (ἄπιστος).