They say not to "pull" mushrooms if you want more in the future. The thought is you will pull out the mycelium (roots) but they are a vast network and chances of that are very slim. There is a much simpler reason to cut mushrooms at the base instead of pulling them: It keeps the dirt out of your mushroom basket. You want to try to avoid washing them if you can so keeping them clean is a great start. At this time of the year you can find: black trumpets (absolute favorite), various boletes like the king and chrome foot and smooth stalk, puff balls, giant puff balls, chicken of the woods, fall oyster mushrooms, hedgehogs, maybe the odd yellow chantarelle and lobster mushroom (although it's getting a bit late for them).