Well having minions push with you when you are attacking is a hell of a lot faster to neutralize/capture points than it is to do it by yourself. From a defensive stand point not only do you not want to have them push with their minions but you may as well make a dollar or two while you stay near your point. IMO it is much smarter to push the next point with your minions than to essentially bd a point. The only time imo you should capture a point is after one or several kills where your team has an advantage or take minions to your equal team fight.
XI Wiki



