There is no good medical reason for a female athlete to wear a groin cup. Some leagues or coaches follow the exact letter of the rules that state all players must wear cups. But girls playing contact sports are not in danger of having their genitals struck because their genitals are protected by being on the inside-unlike testicles which are in fact organs that hang outside, are extremely sensitive, and especially vulnerable to painful trauma.
Note: In some activities such as Martial Arts or hockey, some girls and women wear a groin cup-like protector called a pelvic guard or "jillstrap." This does not protect her labia so much as protect against a traumatic blow to her pelvic bone.
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To protect their gonads from injury.
Answer: If you play a sport where you could get hit in the testicles, you should always where a groin cup. If you are a girl asking this question, the area between our legs is where the biggest differences are between females and males, and you don't need to use a cup because your sexual organs are on the inside, protected by your body. The genitals of boys literally hang outside (the testicles are there because they need to be cooler than body temperature to make sperm, the penis is out there so that it can get erect to penetrate a woman's vagina during sex to deliver the sperm). All this is needed to understand why guys need to use a hard cup and a jockstrap whenever they might get their testicles hit (which are the most sensitive and vulnerable parts of the body), but why girls don't.
Also: Girls can wear a "female cup", but its more like a pad that is shaped to fit between their legs to protect the labia (and is not really a cup because it doesn't need to go around big external organs like testicles). A better name is a "female groin guard" that some people call a Jillstrap (opposite of a Jockstrap)