Basic market understanding, are half the trades of the day short ?

Question might seem stupid but I am trying to get a better grasp of how the market fundamentally works more specifically the equities market. We often hear it's shorts vs longs (bull vs bears) but is it really ? Doesn't that mean for each long there is a short seller ? (if we take out of the equation short cover buy activities and long sell orders). That would mean approx half the trades for a given day are short and the other half are long ?

I was under the idea that there always more longs than shorts for a given day. The market, in theory, can function without shorting being possible. It would be a game of musical chairs.