[jarvic]

The issue is when people (seemingly) randomly switch between he/she and his/hers, even within a single context. Then you end up with something like:

"If your child is in the kitchen, make sure she doesn't touch the hot stove. If he does, however, ..."

Even when the switch isn't that abrupt, if someone is switching between he and she every few paragraphs, it can become very distracting. Using singular they solves this problem.

[dfxm12]

I agree, but that's not what's happening in this article though.

Each bullet/item in a numbered list is a new context.