Why do we need software testing? [on hold]

I have no idea on software testing but intuitively, I can not figure out the meaning of software testing and why we need to do it. In my opinion, a software should first have is function specifications(the need of the client) then the software developers write codes to fulfil the specifications. For example, in the specifications, we say that "when the client type his name in the input box, all the names of his family members appears on the screen".

So during the development, the developer can naturally write the right code to implement the function listed above.

The developers do the same thing for all the functions detailed in the software specifications(developers write codes to implement the functions and developers make sure that it works by debugging it)

So in this way, I cannot see any reason for the testing procedure. Anyone can tell me if my reasoning is wrong and explain the necessity of test by real examples

Thanks a lot!