That "de" should give the idea of subtraction.
"Dequalificante" takes away your heritage ("qualifica"), "debilitante" makes you weak, takes away your power (or health, also).
The idea of subtraction or, in a certain way, of something descending (hence, also in Englishs words that come from Latin!), comes from Latin which "de" is used with ablative case to mean a high-to-low motion (among other meanings).
Take for example in English "deregulation".