Why would leveraging make it better to buy your principal residence with a mortgage rather than cash?

A friend told me that I would be better off buying my house with the mortgage because of leveraging but I can't see the logic? As an example with a house worth 200k you could either

Pay 50k deposit
Get 150k mortgage
Eventually pay it off and sell later for 300k
Which gives a profit of 100k (But would be less in reality with interest payments)

Or pay entire 200k with cash
Sell later for 300k
Which gives a 100k profit

With the mortgage you still end up paying 200k, so what is the advantage of leveraging? Can anyone enlighten me?

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