to push something away from yourself: to shove a person off, and so to refuse or cast aside
The word is built from an ordinary Greek verb for pushing, with a small piece in front meaning "away." Every New Testament use is in the form that turns the action back on the one doing it, so the picture is not just a push but a push away from yourself. Whatever gets pushed was close enough to touch, and the one pushing wants distance from it.
That physical picture is still visible in the first use. In Stephen's speech a man in the middle of a fight shoves Moses off and asks who put him in charge (Acts 7:27). Twelve verses later Stephen reaches for the same word again, this time for what the whole nation did to Moses (Acts 7:39), and the shove has become a refusal. The two uses standing that close together are the word's whole range in miniature.
From there the thing pushed away can be anything a person declines to keep near: a message being preached (Acts 13:46), or a clear conscience someone was carrying and decided to throw overboard (1 Timothy 1:19). Twice God is the one who might do the pushing, and there the word carries an old promise with it. The Greek Old Testament used this verb for the pledge that the Lord will not push his people away (Psalm 94:14; 1 Samuel 12:22), and Paul puts the question in exactly those words before answering it with a flat no (Romans 11:1 and 11:2).
Greek has other ways to say that something was turned down, and each names a different act:
- ruling something unfit after looking it over (ἀποδοκιμάζω)
- setting aside something that had standing, such as a rule or an agreement (ἀθετέω)
- refusing to admit any connection with a person (ἀρνέομαι)
This is the one that keeps the hands in it.