A Reader installation cannot remove an Acrobat install by design. If you need to remove Acrobat from machines you can use one of the prescribed methods in a pre-Reader Install script.
Windows cmd line and msiexec — Enterprise Administration Guide
Silent uninstalls
A silent removal runs without any dialog boxes to show the user that the removal is running. All products use the same command line and the same installer file for silent updates:
msiexec /x {[Package Name | Product Code]} /qn Note
You must include the braces in the command line. An MSI package name (e.g. AcroRead.msi) can be substituted for the Product Code. For Acrobat products, the Product Code is the GUID.