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If Upgrade requirement isn't met, then it means you don't have the initial version of "whatever" installed or its version isn't correct for an upgrade. Sometimes, you just can't upgrade a version without intermediate upgrades. In those instances, a complete uninstall of the old and an install of the new is best.
Of course, this depends on what you want to remove and what you have to install
The message can be displayed for one of the following - let's use Desktop 10.8 as the example of what you are trying to install. you could get that message if you have Server or ArcGIS Engine installed that are NOT version 10.8. you could also get that message if you have ArcGIS Desktop installed but it's a beta version and not a released version. Check your add/remove Programs list and see if you have other ArcGIS products already installed.