I'm the sole user and have always been the sole user of my Mac and have the sole Administrative password. So why would some files be closed to me, (and to Avast!), creating "Error 13"? Something strange going on? 
Thanks!
Because that's the UNIX philosophy, since ~1970s. Even ~30 years later, Windows's implementation of access control layers isn't as useful as this one

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It's pretty normal, that some files (for example, kernel extensions, etc.) aren't readable by the user, just by the system. If you want to scan them anyway, change their permissions (apple-i), or scan them as root (administrator account). But, it's for experts only - common user might damage the system easily, this way. Forthcomming version won't bother you with those messages by default.
regards,
pc