Binacle heads do not ever despise their rock-mates, like Dodrio heads or other multi-brained pokemon often do, but they have fooled many an observer. For although Binacle will frequently bicker with one another, this is simply a matter of culture and pride; each Binacle believes itself to be the greatest, and they are in constant competition with even their closest friends. And most Binacle get along remarkably well by the standards of attached pokemon; those who genuinely do not get along are allowed to leave, and can quite easily find a different rock to call home and a new partner.
A few have suggested that, because Binacle are genuinely multiple pokemon, it should be illegal to use a rock with two Binacle attached in a single battle. But while Binacle, like Exeggcute, are quite capable of leaving under their own power, they share a poke ball with one another – largely because they are too attached to their shared rock to separate - and are therefore considered a single pokemon for the purposes of competition. Furthermore, Binacle are unevolved pokemon rarely seen at high levels, so the rules committees of top pokemon leagues have viewed them with little concern.
Binacle do not typically value their theoretical independence, but perhaps this is for the best, for they will not maintain it their whole lives. Their evolved form of Barbaracle is made of seven Binacle – three of them pairs who shared rocks with one another, and one loner too proud to share its rock with anyone, but accomplished enough to be accepted as a leader and literal head all the same. And no matter what quarrels develop, none of them can ever hop away.