You pat an 8-badugi, opponent draws one and then pats. They may have made a better badugi. Breaking your 8 to chase a 6 is situational.
'When breaking makes sense' (Badugi, G1): Keep smooth three-card Badugis (A-2-3 / A-2-4 rainbow) and draw one. Break pairs immediately. Don't keep a suited junk 'cover.'