(Recap: I founded the curl project, I am still the lead developer and maintainer)
When asking curl to get a URL it'll send the output to stdout by default. You can of course easily change this behavior with options or just using your shell's redirect feature, but without any option it'll spew it out to stdout. If you're invoking the command line on a shell prompt you'll immediately get to see the response as soon as it arrives.
I decided curl should work like this, and it was a natural decision I made already when I worked on the predecessors during 1997 or so that later would turn into curl.
On Unix systems there's a common mantra that "everything is a file" but also in fact that "everything is a pipe". You accomplish things on Unix by piping the output of one program into the input of another program. Of course I wanted curl to work as good as the other components and I wanted it to blend in with the rest. I wanted curl to feel like cat but for a network resource. And cat is certainly not the only pre-curl command that writes to stdout by default; they are plentiful.
And then: once I had made that decision and I released curl for the first time on March 20, 1998: the call was made. The default was set. I will not change a default and hurt millions of users. I rather continue to be questioned by newcomers, but now at least I can point to this blog post! 🙂
About the wget rivalry
As I mention in my curl vs wget document, a very common comment to me about curl as compared to wget is that wget is "easier to use" because it needs no extra argument in order to download a single URL to a file on disk. I get that, if you type the full commands by hand you'll use about three keys less to write "wget" instead of "curl -O", but on the other hand if this is an operation you do often and you care so much about saving key presses I would suggest you make an alias anyway that is even shorter and then the amount of options for the command really doesn't matter at all anymore.
I put that argument in the same category as the people who argue that wget is easier to use because you can type it with your left hand only on a qwerty keyboard. Sure, that is indeed true but I read it more like someone trying to come up with a reason when in reality there's actually another one underneath. Sometimes that other reason is a philosophical one about preferring GNU software (which curl isn't) or one that is licensed under the GPL (which wget is) or simply that wget is what they're used to and they know its options and recognize or like its progress meter better.
I enjoy our friendly competition with wget and I seriously and honestly think it has made both our projects better and I like that users can throw arguments in our face like "but X can do Y"and X can alter between curl and wget depending on which camp you talk to. I also really like wget as a tool and I am the occasional user of it, just like most Unix users. I contribute to the wget project well, both with code and with general feedback. I consider myself a friend of the current wget maintainer as well as former ones.