I think this partly stems from the term "Bitcoin" itself, since coins are not divisible (having moved beyond pieces of eight long ago). But there are no coins in Bitcoin! It's all just txouts and txins.
You can think of it as a magically valuable liquid flowing down a system of ever-growing pipes representing the blockchain where the transactions are linking points and txins and txouts are pipes with their cross-section areas corresponding to their respective values. Once you think about it, the analogy fits perfectly.