I have no kids, and I think a teenager is a bit different then a child. So I will start on what is not exactly the topic, and move from there. I think that a kids computer should always have monitoring software, before becoming a teen (so the teen should expect it). And it is not only a matter of trust of the child as an issue, but also the kids friends. For example my niece (who is 8), had a friend over who tried going to
www.sex.com. The monitoring software found out, they spoke with the parents, etc.. and in the end no foul happened, but without the watch guard she could have seen stuff at that age.
As a teenager, it depends a lot on your relationship with the kid. You have to think for a second how teenagers think. Most teenagers by the age of 14-15 think they know everything. As time goes on they will realize otherwise. If you never had any safeguards on they might totally rebel and get upset about it.
But as someone who was a teenager in the beginning of the internet stage, I will say my kid will have monitoring software on it.
I do feel that we are supposed to filter and shield are kids from stuff in the world. It is knowing how to limit exposure of items that we feel are 'unhealthy' for them at their stage of life, until they are ready for it.
How to react at this point is based on how your relationship is with the kid. If you never had rules and all of a sudden do a 180 the kid will rebel. You know your kid best, but whether you can just put on the software or need to take baby steps to get there, you should know best.