The guy is doing okay -- his income is somewhere over $200k/year -- but this expense is a _big_ fraction of his total income. For him, childcare costs are basically the difference between leasing a new Ferrari and living in a mansion, and buying clothes from Ross and begging his parents for money. (Which, I've learned, he does.)
There are two factors in play. First, he lives in a large and diverse American city, and wants to insulate his children from bad influences. Second, he's under a great deal of, essentially, peer pressure to "Keep up with the Joneses" -- in other words, to keep up appearances relative to other members of his social group.
It's insanity, of course.
But, in his position, it would be difficult to raise a child cheaply. The outcomes might be quite poor. So, either way, there's difficulty and worry.
There are also the opportunity costs of parenting, which are considerable, but that's a different matter.