Anyone can be a copywriter — all they have to do is say, "I'm a copywriter."
There are no certifications or qualifications required. Deciding to be a copywriter is 95% of the work. So when people say, "I want to be a copywriter" - the only thing stopping them is themselves; specifically, their level of confidence in their ability to write and sell.
There's a lot of mystery about what copywriting's about. When I meet someone at a conference and say that I'm a copywriter, their eyes light up - as if I'm saying I'm a magician from Hogwarts. But, really, a copywriter is simply a person who likes to write, does it often, and finds ways to make whatever product or service they're writing about exciting. If we look at it in the lens of supply and demand, words are demanded and copywriters supply them.
Of course, copy is more than just words. It's the meaning behind why people use the particular words they use. Also, people don't just become copywriters to write — they want to also make money. But, here's the thing — in the journey of making money, copywriters often forget that the number one thing that copywriters do: write.
This is why the best advice I could give aspiring copywriters is this: write more and write more often. Because if you're not in the habit of writing for yourself, you'll have a hard time writing for others. However — if you enjoy writing and you write regularly, writing for others — and getting paid — will be a passive side effect to your life.