I need to add this, because I don't want anyone to think I'm trying to be holier than thou or a hypocrite.
My 4th child, Cameron, a toddler/preschooler at the time, was the most vicious and determined biter I have ever encountered.

I was very involved with kids when mine were young, ran my own child care facility, and later a private school, so I had lots of exposure to other kids, and a lot of experience dealing with them. Cam had been raised no differently than the other kids, none of whom exhibited that kind of aggressiveness. He was a sweet child in other regards, and probably the most intelligent though they're all very bright and test high. He was also very high need.
Dealing with him tested every bit of both my patience and my child rearing approach and philosophy. I realized that he bit another kid only when faced with a conflict that he could not otherwise resolve....i.e. you have my toy and I want it. You're pushing me. Etc. Recognizing that it was a reaction to a conflict rather than overt aggression helped me tackle it.
Regardless of what caused it, I still had to deal with it. I went through a period of just under a year where whenever we were in a group of other kids, (playdates, birthday parties etc.,) I made sure before we got together to warn every parent there that my son bit, and bit HARD, and to be very alert. I wanted their child protected, but I also didn't want to exclude the rest of my kids (I have 5 remember?) from every get together by always staying home or never inviting any other kid over. And meanwhile, working HARD on Cameron's conflict resolution skills.
I won't say I never got angry because I did. I won't say I never reacted to his aggression, because that would be a lie too. It was the most frustrating behavior of all my kids. I did the very best I could under very trying circumstances, and worked with Cameron to improve his conflict resolution skills, reinforcing every day that biting was NEVER OK, and that he needed to come get me if he felt pushed into that kind of a reaction, meanwhile never relaxing for even a moment when he was with a bunch of kids so I could intervene and redirect. And over time, whether because of my parenting or because he just aged out of the behavior, it stopped and I stopped having to be hyper-vigilant.
Cameron is a well adjusted, emotionally healthy 35 year old. He is a computer programmer and web developer, earns a 6 figure income, has a lovely girlfriend who is a teacher, a large circle of friends, just bought his first house, and is "normal" whatever that means lol! I've asked him about his biting when he was little, and he vaguely remembers it, and the only thing he can tell me about it is that he just remembers being scared and that was his way of dealing.
I have no way of knowing if my approach helped him or not, if he'd have stopped sooner if I'd punished him (other than removing him from the other kids for a time till he calmed down because he always cried when he bit) or whupped him or put him in time out or whatever.
But I'll tell you this....learning that he bit because he was scared? And knowing that my responses didn't feed his fear, make things worse, cause him to internalize what was going on with him emotionally? That to me is priceless!