They think something along the lines of "The internet must not become a law-free space! We must not allow for villains to be able to do their deeds unhindered in this 'internet'!", and, tragically, they actually believe it.
You see, up until recently, "free speech" was only "free as in law permits". If police was to read your snail mail, they did it -- all it took was tearing the envelope apart. If they wanted to listen to your phone conversation, they did it -- all it took was tapto your line. All they had to do is justify it in front of the law one way or the other...
Now, thanks to advanced digital encryption, if you choose to have a private conversation, it is *truly* private. Simply "ripping the envelope" and justifying it afterwards won't do it anymore... What we have now is truly FreeSpeechByTechnology, not FreeSpeechByLaw.
Now. From your point of view, the change is small: You previously thought you could communicate freely (because law guaranteed you to), now you still think you can communicate freely (because technology guarantees you to).
But from the legislative/executive point of view, the scenario changed dramatically: previously, they could, if they chose to, listen to your conversations. Because laws can be broken, bent, or re-designed, in case that it seems fit. However, now, whatever happens, law enforcement cannot listen to your conversations, because proper encryption cannot be broken.
That's what governments are thinking... But that's not the interesting question.
The interesting question is: You understand why even the most liberal western governemnts react as they do at the perspective of not being able to snoop on your communications. Now, what do you learn from this fact about the way the used to be able to snoop on you prior to you being able to properly defend against that? What does it tell you, that, in whatever extent they used to snoop your communications, it makes them this scary to loose that ability, that they feel the need to pass the legislation they do?