Why should test Web service when web test automation is capable of covering even the functionality?

I'm new to testing. So let me know if I'm asking the question in a wrong way. I'm just curious about Web service and web automation testing.

Example : If there is a web service for calculating the sum two values and also a web page developed using that web service. Using the web automation it's possible to test the UI as well as the functionality of it.

So my question is, what is the point of testing web service separately?