Increased biting — along with several other symptoms such as general irritability and sleep disturbances — is indeed one of the common teething problems and a sure sign that your baby has one or more teeth cutting through. 
Teething pain is a natural part of a teething process. The timing of the first tooth depends on heredity, but in most cases, it appears when the baby is around five months of age. Gum discomfort is in main part due to the pressure exerted by the tooth crown breaking through the sensitive gum tissue. 
Why do babies bite on the nipple?
Well, the reasons are many; they may be irritable, bored, in pain, or just want to try their new chewing tools. There's also a so-called „biting for attention“, which is usually the case with older children. Pay attention to your child when he's nursing — they love their mommy's gentle look and cuddles while having their lunch.
Research has shown that breastfeeding promotes bonding, and can protect a child against internalizing behavior problems later in life. Breastfeeding releases prolactin and oxytocin — both associated with lowering levels of maternal stress and are proven to enhance bonding between mother and a baby. [3, 4]
How to make my baby quit biting?
In most cases when the baby bites the breast, it’s because of the improper latch. You should help your baby to latch properly; it’s for the sake of both of you. A good latch is when the baby has more than just the nipple in her mouth. The lower jaw and tongue should massage the pools of milk from the lower part of the areola. If the baby is latching well, not much of the areola will be visible below the lower lip. [5, 6]
Many children try using the nipple as a teething toy. Pay attention to the time when biting and near misses occur — if they occur at the beginning of a feeding session, the baby is probably not hungry enough and just wants a teething ring. Also, if the biting occurs towards the end of a feeding session, it could mean that he's full and bored.
My daughter started biting when she was about 11 months old, and I feel lucky because it was the time she started understanding more than just the basic commands such as „no“. She stopped because I was gently repeating „no, baby, no teeth“ and praising her with "bravo" when she'd stop. She never did it to hurt me, as it was a gentle and playful biting, but regardless, I wanted it to stop before she brings out the real stuff.
I've noticed she'd use teeth when the milk flow got slower, I guess it was her way to tell me she wants more. Also, it never happened while lying down as it's our common breastfeeding position, but she would bite in any seated position.
I'm optimistic that she's done with biting even before it started for real because she's a big girl now — she's thirteen months old at the time of writing this piece — and she definitely realizes that biting brings pain. I've even had her bite her own fingers and playfully bitten them myself a few times to have her grasp the idea of „pain“. We now share a "no, no" and a giggle whenever she tries using teeth on me. Children learn from first-hand experiences .
The bottom line
Be gentle with your baby even if he's bitten you hard, never raise your voice as it may scare him and make him hate the breast. Be supportive and encouraging in the moments when the baby becomes aware of her teeth as going through the teething pain is certainly not easy for her. Even the youngest children can learn to nurse properly when they hear loving encouragement.
Never ignore the biting, as this is the first step towards spoiling the child. When you let him be his way, he may end up having tantrums and may become a mean toddler. When spoiled kids become teenagers, they’re more prone to developing anxiety, excessive self-absorption, and lack of self-control. According to a psychologist and author Dan Kindlon, if you let your children have whatever they want, they can get to a point where they can’t get real satisfaction from anything.