Is it wrong to monitor your childs text messages?

If the parents pay the bill then yes... if the child refuses stop paying the bill.

What do you have to hide, if there's a text message you don't want your parents to see then theirs a reason why they shouldn't see it and in all honesty that's probably a REASON for them to see it...

If you had a chat with your best friend where she admitted to you that she had been raped last weekend and she wanted to keep it between you two, would you like your parents to know about this stuff? (Of course, she has told the police and her parents, else you would have done it for her.)

If there's no reason a parent should have worry about what a child texts then they'll stop checking the messages. In all honesty a parent would only check the child's message if they think there's a problem.

You're jumping from should to would here, which is not really a good thing to do.

Besides, there is no absolute answer to the question "When do parents think there's a problem?". If a girl has her period, or her boyfriend broke up, she would react with more negative emotions than normal. The parents would usually think that there's something behind all of this, and check her text messages. Voilà! Now your parents might look through your ex-bfs preferred sex-positions and discussions around why he felt that you weren't the right for him. As this is natural in a teenager's life, do parents need to learn about this?

As a final note, if you think your child has a problem, I would assume the best thing to do is ask if there's anything wrong. If yes, don't ask what the issue is, but ask what you two (parents) can help them with.