The answer to this question is hidden right in the word “indirect method”.
When we prepare statement of cash flows using indirect method we have to use income statement to find out the cash flows indirectly from it.
Now, we can understand that the basic purpose of Income statement or Trading and Profit & Loss account is not to summarize the cash flows of the business but to present the incomes and expenses earnt and incurred during a particular period. We also know that income statements are prepared on accrual basis i.e. incomes and expenses will be recorded as and when they are earnt and/or incurred as opposed to when they are received or paid respectively.
Thus the incomes and expenses given in the income statement include such amounts which are payable and/or receivable. Therefore not the whole amount of income and expense should be considered as a reflection of cash inflows and outflows.
For example, if a carpenter has repaired something and has charged 100 for it but customer gave just 60 and promised that he will pay the rest after a week. Now, in this example even though he has earnt 100, as he has done his part of the job, the cash inflow is of just 60. Meaning that in cash flow statement we will consider only that amount of cash that actually flowed in or out of the business.
That is why we subtract interest incomes to the profit because they usually contain the accruals and we add back interest expenses for the same reasons. And later we include only that amount of income and expense that represents actual cash flow.
However, depreciation is reversed for some other reason. Even though we charge depreciation as an expense, business never pay anything in this regard to anybody i.e. there is no cash outflow for this expense. It is just an estimate of loss of value in the asset because of its use. So, this is not a real cost instead just a notional cost (presumed cost). Therefore all such costs and expenses which are not real but notional in nature and are not backed by cash flows are reversed in the income statement to reach at the correct amount of actual cash inflows and outflows.