My 6 geared Shimano bike doesn't shift from higher to lower gears but does the opposite smoothly My 6 geared(Shimano gears) mountain bike with the grip shifting system shifts really smoothly from the 1st gear to the 6th (biggest cog to the smallest). However when I try to twist the shifter from the highest gear to the lowest, the grip feels tighter and tighter and then gets impossible to shift at the 4th or 3rd gear. 

Stuff you may need to know:


Pressing against the derailleur with my thumbs manually changes the gears perfectly.
Removed the cable from the derailluer to check the shifter itself and it pulls and pushes the cable perfectly too.


Please help!
Separating the derailleur and shifter by undoing the cable is the correct diagnostic process. You now know the derailleur articulates freely, and the shifter shifts freely also. 

Next step would be to pull the cable at the derailleur end while working the shifter to see if tension produces friction or binding in the cable and housing.

Also closely inspect the cable run. Make sure that the housing is inserted into frame bosses properly. Look for kinks in the housing, runs of housing that are too short or anything where the cable might bind up  Pull the cable out and check for kinks or fraying.