Statement of cash flow

Dear Tutor,

I was wondering What could be the logic behind subtracting an increase in inventory under the changes in working capital.

I was thinking maybe it’s because it’s purchases which involves an outflow of cash. But inventory in itself is not a cash item. So as an increase in inventory (closing-opening) reduces cost of sales, this will increase profits. As a result we will have to remove the amount from profit to be able to calculate the cash flow.

Is this reasoning correct Sir