Answer:
A dragon's tooth in a mortal's hand, I kill, I maim, I divide the land.
They make no sense at all, In them you either fly or fall. They make you do it all. Their need is biologic, but they are most illogic. They are not real but still can be achieved, If they are just believed
In buckles or lace, they help set the pace. The farther you go, the thinner they grow.
Just head and foot yet never tires of dancing.
You heart it speak, for it has a hard tongue. But it cannot breathe, for it has not a lung.
If itβs information you seek, come and see me. If itβs pairs of letters you need, I have consecutively three. What am I?