Why is the gum around my molar bleeding when I brush it and what can I do to stop this?

Many causes. Most common reason is because it is inflammed (gingivitis) due to plague and bacteria. In addition to brushing you need to floss as well. Use oral antiseptics as adjunct. Talk to your dentist. They may recommend waterjet. Also, make sure you are using a soft bristle tooth brush so you are not traumatizing the gum.
See your dentist. Either you're brushing too hard or you have gum disease like gingivitis. You should see your dentist about this.