The essence of learning is making mistakes, that's HOW you learn to do it right!
I have to say, I don't agree with this. We learn to do it right by doing it right, not by doing it wrong. When you do something wrong, it means you haven't learned how to do it right yet.
Is it impossible for someone to do something right without doing it wrong first? No, I don't think so. Getting it wrong is not a prerequisite for getting it right.
You can make mistakes forever, but that won't lead to learning how to do it right. Listen to long time immigrants who make the same mistakes again and again. There's a term for it, called fossilization.
So how do you learn to speak a foreign language correctly? More than likely, by paying attention to how native speakers speak. You focus on good examples and use those as your model. If you do make a mistake, just ignore it. Your mistakes won't help you improve.
Why do people make mistakes in a second language? They make mistakes when they don't have the proper framework built up in their head and they try to output language. Basically, they are speaking too early (or too much). You can say what you know how to say without making any mistakes. When you go into unknown territory, that is where you make mistakes.
Mistakes by themselves are not bad, but when you keep repeating the same mistakes, it develops a pattern in your head which, to you, starts to sound OK. This is the only danger of making mistakes (besides being laughed at).
If you follow a "practice output" approach, be sure to only use correct language. Practicing output should not be done by making up the language yourself as you go. Do not practice free conversation unless you can and are good at controlling the conversation. Otherwise you'll be asked questions that you can't answer correctly and you'll start making up language to try to express yourself.
Don't make the mistake of making excuses that sound like the one in the quote above.