"The New York City Ballet is always about the realm of possibilities, the realm of what the human body can do, what the human spirit can do. And it's about listening, it's about listening to remarkable music and how we respond to that." John Guare
"Often ballet teachers find the specifics of training the foot strength needed for pointe work difficult as it came naturally to them. However for many people, the isolated strength needed in the feet must be specifically trained, especially nowadays, as many children who grow up in cities spend little time bare foot on different surfaces, which naturally trains the tiny intrinsic muscles of the feet. Understanding how these muscles should work when dancing is imperative in a long, injury free, career in dance." - Lisa Howell
In addition to intrinsic muscle weakness, the foot and ankle can suffer other injuries. Floors built on concrete are a source of injury, even for dancers who are taught to "come down through the foot". This technique helps, but does not fully compensate for hard flooring.
Any repetitive motion can lead to injury.
Some ankles and achilles tendons will build up soft tissue mass or calcified masses from pointe shoe ribbons being tied tight. I won't say "too tight" because dancers tie them tight as needed.
Some ankles won't like the repetitive releves and jumps required by dancing and will build up some type of tissue resistance at the front of the ankles. This extra tissue will cause disruption to the movements, or pain, or both.
ANY incorrect technique such as rolling ankles, turning out the foot more than the leg (a requirement in ballet), too short pointe shoes, too narrow pointe shoes, insecure demi-plies,(heels not on the floor, leading to sliding heels too far forward, usually, resulting in tense ankles, tibial muscles [ shin splints]), - and you go up the body from there, straining knees, hips, low back, raising shoulders, straining neck, clenching jaw, locking cranial bones, headaches - need I say more?
However, the human body can repair its tissues, especially with the help of good nutrition. Whole food supplements for collagen, ligaments, and muscle can be added to the diet. After a fracture, raw veal bone meal and correct calcium supplements can speed healing greatly.
An excellent topical ointment called Traumeel can help soft tissues heal.
Icing and diet can assuage inflammation. No one is "stuck with" an injury. All athletes have the internet to refer to, to add to what their own doctors, chiropractors and physiotherapists tell them about injuries.
Ballet is very competitive. If you get an injury, don't become panic stricken. The next exam or performance does not matter as much as all the years that come after that.