Whenever we talk, it immediately turns into an argument.

Literal

Talk [object-を] do-[when-と] immediately argument [into-に] becomes.

The conditional と here marks a habitual, automatic consequence: every time conversation starts, arguing follows. 口論 (こうろん, 'quarrel') is a more formal word than けんか. すぐに ('immediately') underscores the inevitability.