I think it would be odder were it otherwise. What you say fits perfectly into the (rightly, very vague) picture which Dave evokes: the words for “beech” and “book” are similar in several Germanic languages (German and Dutch as well), of which I believe Swedish is one.
In Romance languages (Spanish, French, Italian, Portuguese), on the other hand, the words for “book” and “beech” are related to the Latin words liber and fagus respectively.
Dave mentions the hypothetical use of beech bark as an early writing material. I would suggest the wood of the tree as a much more likely candidate: it’s much tougher and more durable than bark, lighter in colour, and (unlike the bark) can readily be given a smooth, flat surface. There is lots of archaeological and literary evidence for the use of wood as a writing material by many cultures. In Roman times, ephemeral writing was often done with a sharp stylus, on wooden tablets covered with a surface layer of wax. The tablets could be cleared by warming, and then cooled, and used again. When they wanted a more durable copy, the Romans would use papyrus, parchment, metal, or stone
Pipped by Dave (hardly surprising ;-)