打ち合わせる means “to arrange a meeting” or “to agree on something”. I clearly see the
合わせる part signaling an agreement. Yet however I can’t see where the
打つ part became something other than “to hit”, “to strike”. Does this verb has a canonical meaning that would together with
合わせる clearly make this non-physical meaning?
This article recommended by @aguijonazo explains the etymology.
The term comes from court music, where wooden sticks were used to set rhythm for all instruments. Originally,
打ち合わせ referred to clapping (
打つ) of those sticks used to make the rhythm match (
合う). The meaning then generalized and the word is now used for preliminary discussions that ensure that all involved parties are on the same page.
Early on, I would joke with people about 打ち合わせ (the noun) as people with a disagreement punching it out to determine who was correct.
I generally consider this to be like 'hammering things out' in English.
My experience over the years has been that just as the parts of English words do not always carry one exact meaning, the meaning of individual kanji in combinations have many variations.