I had a physics teacher in college who explained it like this.

Imagine we see by throwing tennis balls. You know the shape of something (and he gestured at a giant whale skeleton in the lecture hall) by Knowing where the tennis ball bounces off of the shape. If we throw a lot of them, we can "observe" the shape of an object.

Now imagine the object we want to observe is another tennis ball. With the skeleton, the tennis ball, even meant of them, hitting it and bouncing off won't effect it. But if we want to use our tennis ball sight to observe a tennis ball, it's going to knock the tennis ball away, thus we've significantly effected it.

The only way to "observe" a photon is to use something that will have a significant effect on it.

This was some 15+ years ago, so I might be misremembering the details slightly, but that was more or less the gist of it.