juz wrote:my son headbutted me at 4 months and drew blood....
Same here, my daughter headbutted her mom when she was 4 months old and drew some blood.
I started teaching mine certain things: how to properly make a fist, I do smilie situps with her hoping that this will get her accustomed to roll a bit when she falls backwards and I also started rolling her over the shoulder (mom does not like it - it has to be approved by a pediatrician).
I believe that martial arts hold many benefits for kids in terms of good movement principles (efficient biomechanics), attribute development (strength, stamina), body awareness (improved proprioception), reflexes that may prevent or lessen injuries (like rolls, breakfalls and yielding). Martial arts sessions can also be used to impart certain values regarding self-defense as well as teaching protective behaviour: what to do when approached by a stranger or when one is bullied or bothered by other kids or even good old peer pressure. In fact, martial arts are a great opportunity to talk about violence and build a foundation to help the child become more self-confident and therefore less likely to fight.
Of course, you can do the above outside martial arts, but martial arts present a convenient teaching package. Obviously, you do not teach kids the things that you teach adults: you withdraw certain dangerous techniques (neck breaking is a big NO-NO), you do not talk about certain issues like killing while you should talk about things that adults take for granted like what to talk to adults about trouble between kids, what to do with different types of conflict: insults, sharing of toys etc.
I don't see anything wrong with teaching your child martial arts, if the kid is interested in doing what mom/dad does. It is wrong to push them though, especially since you can teach the same stuff outside martial arts, like Chris and Dave pointed out. However, teaching them some basic things, even certain self-defense stuff to use against bullies, does not take their innocence away as long as it is presented as a fun game, adapted to their age as opposed to a rigid training regimen (and even this can have benefits on certain kids, that need to learn to respect authority).