If we add a weak acid such as carbonic acid in water it weakly dissociates to form bicarbonate and hydrogen ions . Now water already has some hydrogen ions, having a ph=7.
So now indirectly we added hydrogen ions and base (bicarbonate ) ions to water which already has a hydrogen ion concentration. The resulting solution is acidic . This means that in the addition of equimolar hydrogen ions and bicarbonate ions( base) hydrogen ions dominate.
The only reason which I can think of is this: lets say there were 1000 hydrogen ions in water, now addition of 100 hydrogen ions and 100 bicarbonate ions will cause a net increase in hydrogen ion concentration because bicarbonate wont be able to counteract the increase in hydrogen ions because bicarbonate, when acting as a base, will be in equilibrium with carbonic acid. I.e. 100 bicarbonate ions won be able to neutralize 100 hydrogen ions present in the solution, and because of their equilibrium they will ionize only say 50 and overall, and there will be an increase of 50 hydrogen ions.
Is my explanation correct?