Why? Because it promotes a premature knee bend. While a child is attempting to keep the legs together, the fly kick with a kickboard makes it nearly impossible for a beginner to get the core involved. An elite swimmer, on the other hand, who's kick is automatic can handle it, and it can be even really useful to work on tightening those abdominal muscles. But for a young learner, it simply encourages him/her to draw the knees forward, which is a major setback and promotes extreme frontal drag.
Other butterfly or dolphin kicking drills such as side body dolphin, vertical dolphin, and back body dolphin are all great ways to practice kicking. However, I would still save those drills for a swimmer who can already do the stroke legally. I personally avoid them for the swimmer learning how to do the kick, because they are simply too complex at this point in time.
The drill I primarily emphasize with beginners learning how to butterfly is a drill we call the body dolphin butterfly kick. The drill is done in a prone position, and you teach your swimmer to make the butterfly kick one that incorporates the entire body, not just the legs. We use the learning cues Kick the head down, kick the head up. I also like the cues bottom down, bottom up as they really seem to help the young learner get the hang of using the core involved vs. just kicking from the knees down. In terms of getting the fundamentals of the fly kick, I also like to remind my young learners to kick the legs together like one big flipper. I also like to ask my young students to pretend they are a dolphin or a mermaid.
While I don't like to get to detailed when teaching beginning butterfly swimmers, I think it's important for teachers to understand the action of a good butterfly kick. In a nutshell, the legs are fairly straight during the upward action of the kick, and then flex just before the downward action of the kick. The legs continue to accelerate kicking downward until the legs are hyper-extended.
Lastly, when teaching body dolphin butterfly kick, discourage your students from dunking the head. While you want them to kick the head downward to promote the necessary undulation, a kick that's too deep will only slow forward progress and increase frontal drag.