You Can Make Videogames - a handy site created by Richard Perrin, a good place to look if you're interested in making games but you don't know where to start.
No You Can't Make Videogames - don't read this, it's silly.
You absolutely can make games.
(Videogames if you want. There's not a categorical difference. Cardboard is a great place to start.)
I've been making games for as long as I can remember.
My first games were terrible, and completely derivative. "Fan-fiction", if you like. I remember one, Snakes and Ladders with the squares randomly scattered across the board in different shapes and sizes, different instructions written in each, roll and move, no decisions. Another, Chess with all the movement rules changed - no reasoning behind them, just all every different pattern I could think of. Terrible terrible games, but I still had a lot of fun making them (and playing them, when I could convince my always-skeptical parents or siblings to give them a try).
Later, I found a book about BASIC programming in the library and learnt from it. My first videogame was typed in from a code listing in the book. This is as derivative as you can possibly get: an exact copy of someone else's game. But then I tried out changing numbers and seeing what happened, modified it, made it my own - totally broke it in the process of course, made it worse and worse until I reached a point where it didn't run at all and I didn't know how to fix it.
So I made terrible games. But I got better.
Eventually I was able to program my own games from scratch. I made text adventures (not worth being glorified by the term "interactive fiction"), copying ADVENTURE. They were very bad in many ways. The gameplay combined the worst of "guess the word" puzzles, unnecessarily complicated mazes, and brute force solving. But the code, the code.. I had no idea how to organise things, no conception of data structures and algorithms, but I didn't let that stop me. For every single room in the game, I had a separate block of code, with its own input loop, looking something like this:
100 PRINT "You are in a dark maze."
110 IF GOTLASER=0 THEN PRINT "There is a glowing laser gun here."
120 PRINT "You can go south or west"
130 INPUT WORD$
140 IF WORD$="get laser" THEN GOTLASER = 1
150 IF WORD$="south" THEN GOTO 190
160 IF WORD$="west" THEN GOTO 420
170 PRINT "I don't understand."
180 GOTO 100
If you're a programmer, you're wincing. If not, you probably don't see what's supposed to be bad about this. And in a sense, there is nothing bad about it: it worked. There are good reasons for the ways programmers like things to be done; they're less prone to error, they save time once you know what you're doing, they're easier to modify. But when you're just starting out, all that you should worry about is whether something works.
Now, after 20 or so years of making games, I think I'm pretty good at it. I've made some games that I'm very proud of, that I consider worthwhile contributions to the medium (whether others agree or not) - and many more that are terrible, but were satisfying to make. But it's been a long process, and there's still room for improvement, I'm still getting better. You can't expect to change the world with the very first thing you make, but it can still be a step towards it.
If you're reading this, you have access to much better resources than I started with. An internet full of programming tutorials, source code, willing helpful people, and tools that are both much more powerful and much easier to use than a stupid BASIC prompt. You're in a much better position than I was as a kid trying to figure this out by myself.
At the very least, you can make something silly that nobody else wants to play. Why would you want to do that? Because it's fun. It's not easy, it's time-consuming and sometimes hard work, but making your own videogames is the most fun you can have with a computer. Forget playing games, making them is where it's at!
But also, because you'll get better. Everyone starts out terrible at everything, we only improve with practice. If your goal is to make a good game, you have to start by making bad games - it's the only way. When you're doing something that's hard for you, you're not wasting your time. Making games isn't easy, but it's something you can do if you want.
"We have created a situation where -everyone- creates things, all the time."
No we haven't. Not yet. I hope we do though.
More people are creating things, and that's great, but so many are not. They get discouraged because they think they're "not creative" (creativity is not a talent, it's a way of operating - John Cleese), because they think it's hard work, because they worry they'll never be good enough. Don't be discouraged. Creation is good for you: it's worth doing even if you just do it as a hobby and even if you never make anything that anybody else cares about (although you will, if you persist).