Are you using the version designed for use on the face? If so, that is probably the answer.
Skin and hair are very similar. What is strong enough to destroy hair is likely to damage skin.
Hair removal cream designed for the legs is much stronger than hair removal cream designed for the face, because the skin on the legs is stronger than the skin on the face.
Many women have relatively fine hair on the face and a weaker cream can remove that. But for those who have coarse, male-type moustache and/or beard growth, that weaker cream is not going to remove it.
Where you have male-type growth shaving is likely to be a very much better answer.