Surely, it was big 4 because Chelsea, Man Utd, Woolwich and Liverpool WERE the big 4 clubs.
You had Liverpool and Man Utd, two of the most successful teams in history and then Chelsea and Woolwich who by Premier League standards were big clubs at the time. Chelsea were winning titles and domestic trophies and Woolwich had won league titles and competed.
It only turned big 6 when ourselves and Man City started rising to finish 4th (and above) and compete.
It wasn't because those teams finished outside the top 4 at all. Because at times when they did, the likes of Newcastle and Aston Villa had finished in that top 6 and never got called it - because they weren't clubs stable enough to keep it up.
Big 6 is actually a term used to describe 6 of the best teams in the Premier League on either size, history and revenue.
That won't change until Woolwich continuously fall out of that top 6.