Split-pushers win by creating a lose-lose situation: send one person to stop them, and they either kill that person (if it's a squishy) or ignore them and take the tower anyway (if it's a tank). Send two people, and their team wins the 4v3 on the other side of the map.
The counter to split push is not "send someone to match them." It's "force a fight before they can split."
Here's the macro flowchart:
1. If the split-pusher is in a side lane and their team is grouped as 4, you have a numbers advantage. Force a 5v4 fight immediately. Ping your team, engage, win the fight, then rotate to stop the split-pusher.
2. If you can't force a fight (their team is playing safe), send your fastest wave-clear champion to match the split-pusher. They don't need to kill the split-pusher — they just need to clear the wave so the split-pusher can't hit the tower.
3. If the split-pusher is Li Xin in ranged form, you need a diver. Li Xin is squishy in ranged form. Send your jungler or a mobile bruiser to jump on him.
The universal mistake: sending your ADC to match the split-pusher. Your ADC needs to be with the team for the 5v4 fight. Send your clash laner or jungler instead.