The Greek adjective aspondos means irreconcilable or implacable — one who refuses to enter a covenant of peace. Built on spondos (a libation poured in making a treaty) with the alpha-privative: one who will not pour the libation, will not make peace, who remains in permanent hostility.
Paul includes aspondos in his list of end-times characteristics (2 Timothy 3:3) and in Romans 1:31 as a marker of human rebellion against God. Irreconcilability is a profoundly anti-Gospel posture — the Gospel is the proclamation of peace, reconciliation, and the breaking down of hostility (Ephesians 2:14-16). Christ is our peace; to be aspondos is to reject the very nature of the Kingdom. Where the Spirit works, enemies are reconciled and barriers fall.