My toddler is still too young to be a biter, but I used to nanny a lot of toddlers. From what I can see, anytime a child displays aggressive behavior (hitting, biting, kicking) boundaries and consequences must be quickly and firmly reinforced every time it happens. For a 2 year old, that would be immediate intervention with a calm but very firm scolding “no, we do not bite!” and an immediate consequence (time out, removal from the situation, etc). You do not have to yell, but you do need to convey it in a tone that means you are serious - a stern face, lock eyes, a firm voice, no smiling. You have to make sure that every disciplinarian is using the same system….if daddy is being firm, but mommy giggles and shrugs it off, it is confusing for the child. If you only intervene half of the time, or you only remove the child/follow up with a consequence half the time, your scolding starts to mean nothing. Be proactive and talk to any nannies or daycare teachers about the problem and authorize them to use your system so you are all on the same page. This helps with consistency, but it will also help if your kid does bite another child because it will be obvious that everyone is taking it seriously.
I do not agree with the “let's reason and talk about your complex emotional feelings” approach when it comes to toddlers acting in a manner that can hurt themselves or others. This intellectualized approach seems to be based on adult reasoning and cognitive abilities, not a child’s. Cognitively, it seems like very young kids are more akin to animals than human adults, so firm boundaries and consequences work well when it comes to stopping negative behaviors. Sometimes simplicity is best when dealing with less cognitively complex creatures. It may make the parent feel better to talk all about anger and feelings (that way they don’t have to deal with the discomfort of actually reprimanding the child), but I suspect the whole concept is lost on the little one. Kind of like those pet owners who soothe and pet and shush their nasty little dogs when they growl and bite…they think they’re being supportive, but it rarely actually stops the problem (and sometimes makes it worse).