If you cannot get a section of the cover to release, don't force it; move along the cover and try another spot. The cover is held together with internal plastic clips (tabs) and they don't want to let go! Often a stuck tab will unhook as you release the next one.

DO NOT RUSH, and don't push your pick/card/spudger deeply into the laptop as you may damage internal connectors; push the pick in no more than 1 cm (~ .25 in).