Maybe because the messages have been locked or you're not doing the right thing. You have to press a text and it will say more and then you check the message you would like to delete.
First, open the specific message you want to delete and press on it with our finger. A small menu will appear. From there, click "More," then on the bottom left...
There isn't a built-in way to hide existing text messages in iOS, but you can search for apps that will hide your messages by typing "Hide Texts" into the app...