I am never sorry to lose a few parsley or dill leaves to the black swallowtail caterpillar (see photograph above.) There are never too many of them; the most I have ever seen on any plant has been about six. I would never consider them a pest. On the other hand, although I think the fluttery cabbage white butterflies are pretty, I don’t like their egg-laying abilities. A few cabbage white butterflies hovering over any plant in the cabbage family means big trouble, as in the recently shredded leaves of my prized Tuscan Kale.
In the past few days I have hand-picked dozens of caterpillars off of this plant. I think I have caught up at the moment and the plant is free of pests. Where are all my praying mantis predator bugs? I was going to plant a few broccoli plants this week, but now I am rethinking it since they are members of the cabbage family too.
Here is good link to a post about this pest: Cabbage White Butterfly Caterpillar