Why doesn’t text work to only one person?

That could be for many reasons. It could be an issue on your end, or it could be an issue on the receiver's end. Did you have the receiver check to ensure that you are not blocked? Is this person an iPhone user or not? See this for issues with receiving messages. If you can't send or receive messages on your iPhone, iPad, or iPod touch - Apple Support

Another alternative is for the two of you to completely delete the conversation you have with each other and then start a new one.