You can bite straight into a mango, provided the skin is washed but it’s best to avoid eating the peel because it’s tough and doesn’t taste very nice. Also, it may cause an allergic reaction due to its urushiol content. If you want to bite into the mango and enjoy the flesh, cut away some of the peel first, then enjoy eating the exposed flesh down to the peel but discard the peel (and also avoid the pit).