I say it absolutely should go. It's meaningless noise, like including a "Programming" tag on StackOverflow.com, or a "Ubuntu" tag on askubuntu.com.
However, this does raise the issue of how we should retag a couple of the questions that currently have the parenting tag.
This one and this one both have that as the sole tag.
The first one is closed as a dup of this question, which uses learning, but I'm not sure that's the best tag for either version.
Perhaps a more specific parents tag would be appropriate for these, to indicate that the focus of the question is the parent? The communication might be a good addition to the second question.
This question has the parenting and the vague and ambiguous action.
For this, I suggest that we replace both with behavior and communication.