Without automated testing, we cannot do smoke tests, or regression tests, because we have to test new features everyday, so without automated testing we cannot have a full product coverage.
Actually, imagine that you have a good automated test case coverage of your product, today we can find tools that test the product in real time, for example, code analysis tools which resolve dependencies in every developer code check-in and find which test cases must be run in order to report how the check-in impacts in the whole product. This is impossible in manual testing, because a developer can make a lot of checking in a single day, and test engineers must be involved in a higher level, developing tools in order to make load tests, stress tests, and customer oriented testing.
Manual testing also depends on the ability of the person who run the test, how fast he can be, and there are many factors that can delay the testing, such as an illness, or the humor of the person in a particular day.
So, as Harry Robinson from Google Test says:
Life's too short to only use an approach for testing that relies solely on a human's ability to execute a series of mouse clicks and keystrokes when the processing power that makes computers so useful can be leveraged to execute these tests, freeing testers from especially mundane or repetitive testing so that their brains can be used for higher order tests that computers can't do yet.
