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Why does a long/purchased call option have a long position in the option itself?
It will be helpful to establish some definitions: Long "Long" is financial slang for "to have possession of an asset", legally, and "to debit an asset", financially.   Short "Short" is financial slang for "to be liable for an asset", legally, and "to credit an asset", financially. Option "Option" is financial slang for "to have the right but not obligation to force the liable to perform action", legally.  Without limits and when taken to absurdity, this can mean slavery.  For equities, this means "to have the right but not the obligation to force the liable to buy/sell a specified asset at a specified price with a specified expiration for that right" for a call/put, respectively. By the above, a call option is "the right but not the obligation to force the liable to buy a specified asset at a specified price with a specified expiration for that right". By the definition of "long" above, a call option is actually not long the underlying. By the definitions above and with a narrower scope applied to equities & indexes, to be "long" the call means "to have the right but not the obligation to force the liable to buy a specified asset at a specified price with a specified expiration for that right" while to be "short" the call means "to have the obligation to be forced to sell a specified asset at a specified price with a specified expiration for that right". So, to be "long" a call means to simply own the call.