The idea behind minimum wage is that nobody earns a real pittance, everyone gets a reasonable chunk of cash.
What really happens is that if your work isn't worth minimum wage, you can't get a job at all. Since it's age-related, every time you pass an age where it goes up, your chances of getting a job go down.
In this story, the employer behaved appallingly. However, the reason she sacked the girl is clear: the employer would have to raise the employee's salary at age 18 whether or not the employee was worth the extra to the business.
It's not an isolated incident, as the comments make clear, although most employers don;t simply pretend their employees have ceased to exist and do provide a warning of what's coming. If you're doing a job an employer is willing to pay the 16-year-old rate to have done, then when you turn 18, that employer might not be willing to pay more to have the same job done. So you're out and the next 16-year-old in line gets your job. Same job done for the same cost - that's business.
If it wasn't for the minimum wage laws, those turning 18 would not face being replaced by 16-year-olds. We used to worry about being replaced by younger staff long ago, but we never expected to see the day when an 18-year-old would have that problem!
So the minimum wage isn't really such a good idea after all. I know there are those who would say 'So you'd work for less than minimum wage?' and my answer is not only 'yes' but that sometimes, even now, I do. If you look at the time spent writing a book and the pittance books bring in, it works out at less than minimum wage by a long way. It's still better than no wage at all. I also gain experience and I have that work out there so maybe, one day, the return will be above minimum wage. That's called 'working your way up'.
You can't do that if you're replaced at 18, can you?