Presumably OP is talking about a younger kid, and not his 17 year old. It has nothing to do with trust of your child, and has everything to do with not trusting other people to do what is best for your child and not try to take advantage of them. To put it another way, I doubt OP is concerned that his kid is going to go hunt down a pedophile and then have sex with them. He is probably more concerned that a pedophile might try to hunt down his kid and then have sex with them.
I should have mentioned that I am talking about 8-9 year olds.
I'm just some random on the internet, but this rubs me the wrong way. Trust is important in relationships, and this doesn't show any trust. Some of this is perfectly fine, but tracking their chatting is an invasion of privacy unless you have a specific reason to be worried.