Q:

Why can't I step through Java API classes? 

I have set a breakpoint in String class.  On running the program in debug mode the breakpoint is hit but I cannot step into the code.  Pressing F5 resumes the execution to next breakpoint.  I have removed java.*  package from step filters. 
I am using Groovy grails toolsuite instead of vanilla Eclipse. 

Edit:
Eclipse does seem to have source archive:

A:

GGTS has step filters on by default.   Go to Preferences -> Java -> Debug -> Step filtering to disable it.   You also may need to go to Preferences -> Groovy -> Debugger -> Extended debugging and disable all preferences there.