[jimktrains2]

If they're talking about a specific child, sure, but if they are talking about a single, unspecified child, they is becoming more popular[1].

"Bill is over there. He is playing with his toys."

"If your child is in the kitchen, make sure they don't touch the hot stove." vs "If your child is in the kitchen, make sure he/she doesn't touch the hot stove."

For many readers the he/she breaks all flow the sentence had.

[1]: http://en.wikipedia.org/wiki/Singular_they

EDIT: s~he/she don't~he/she doesn't~

[dfxm12]

This is a false dilemma. "He/she" was never even mentioned.

In the context of the article[0], other options exist like:

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

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

These sentences are no harder to read than if "they" had been the pronoun used.

[0] - and I really think what the author is trying to do is make the reader think of a different child with each bullet point. Not a single, unspecified four year old, and not a collective group of every four year old, but one unique four year old for each bullet point. Alternating the gender of the pronoun creates this effect.

[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.