developmentally children at this age are in a stage which they cannot understand other's pain. which is why it is so hard for them to share.
So biting him back wouldn't work because he only wonders why you hurt him, he cannot process that he is hurting others.
My son is about to turn 2 and has also started this.. he is biting very hard... it is scarey.
He knows he isn't supposed to do it because after he does it he covers his eyes and seems to show remorse.
I tell him "NO BITE" "that hurts! I cannot let you bite other children" If it is during our childcare hours we set him on the couch and talk to him about it. with very simple words like I wrote up abvoe.
However when he is upstairs with my husband and I. My husband pops his mouth and tells him NO BITE! that hurts.
He cannot really process that he is hurting other children but he knows he isn't supposed to do it. However, controlling thos impulses is very difficult at this age. Which is why you will probably have to tell him over and over again. Or be there to stop him if you notice it about to happen.
Guidance is a long process but it is far more rewarding for both parent and child when it has a breakthrough...
I have a great example of guidance that worked so wonderfully..
for a botu the last six months whenever we were in the car my daughter would scream when her Dora CD was over. Each time we would put it back on but would also Say" McKenzee you cannot scream for Dora, when you want it back on you must say, "Mommy please put dora back on".
Well, after several times of this over the past six months we had a break through.. She polietly asked!!! I was so excited!!
You see instead of yelling..Don't scream and turning it off. she learned how to act. that is the wonderful part of guidance.. we are teaching them what TO do.. instead of always yelling about what NOT to do...
they weren't born all knowing.. :)
Good luck!