Easy question about depreciation question, actually, studying, around, cannot

hardwork24

To me there seems to be a really easy and obvious explanation for this that I cannot wrap my head around for some reason (maybe too much studying):

Assume:
EBTD is 100
Depreciation is 50
So EBT is 50
EAT @ 50% is 25

After tax cash flow = EAT + depreciation = 25 + 50 = 75

Does this mean that you will actually have more cash ($75 in this case) assuming depreciation expense, than if you had no depreciation (EBTD x EAT @ 50% = 100 x 50% = $50)?

In other words, why do we add back ALL the depreciation when we could add back depreciation net of tax (50 x 50% = 25) to get equivalent cashes of 50 dollars?