I won't let you win! / I won't give in!
'Darla vinta' — DAR-la VIN-ta. 'La vinta' = the victory (the won thing). Stress on each word.
Use playfully or seriously when you refuse to back down in a disagreement. It's competitive but can be affectionate — often used between friends who argue regularly.
'Darla vinta a qualcuno' (to give someone the win) means to let someone win an argument. 'Non te la do vinta' = 'I won't give you the win'. This phrase is competitive but has a playful quality that makes it more affectionate than aggressive.
Non ho intenzione di cedere.
I have no intention of giving in.
More serious — 'cedere' (to yield) implies firm resistance to any compromise
Su questo non mi piego.
On this I won't bend.
'Piegarsi' (to bend) — idiomatic for yielding or capitulating under pressure
Mantieni la mia posizione.
I maintain my position.
Formal version — 'mantenere la posizione' (to maintain the position) is debate-standard language
Italian debates can be extremely competitive — not just about reaching truth but about 'vincere la discussione' (winning the discussion). This competitive streak is balanced by the tradition of accepting defeat gracefully when shown to be wrong. The important thing is that the argument is well-fought.