瓦 is fired clay — the radical of pottery. 并 lends the sound. A 瓶 was a clay jar for water or wine long before glass; the character survived every material change, from celadon vases to plastic water bottles.
The 花瓶 flower vase carries a homophone blessing: 瓶 píng sounds like 平 peace, so a vase in the home means 平安 'peace and safety'. Called someone a 花瓶, though, and you've said they're decorative but useless — beauty without function.
Clay 瓦 vessels standing side by side 并 — BOTTLES on the shelf.
瓶颈 'bottle neck' migrated into Chinese exactly as in English — the narrow point where progress chokes.