It's been awhile since I tackled this issue but.... there are "default" clothes/armor that some NPCs have that you cannot see when you look at their inventory, and therefore, you cannot remove these items through a trade or other means. For example, Lydia wears a default set of steel armor, so no matter what other armor or clothes you give her, she won't wear anything else but the default steel armor (unless what you give her has a higher armor rating than Steel armor...). Note that you also will never 'see' her default armor in her inventory.
I haven't tried with Faendal, but I am assuming he has a set of default clothes as well, and you don't see them in his inventory. Thus pickpocketing his clothes might be possible, but when you give him another set of clothes to wear, the game simply resets to his default set instead.
If you gave him armor to wear, instead of clothes, however, he should wear the armor. Try leaving him (dialogue option to either Wait here) and then travelling to another area and returning to him, and see if that works.
Finally, if you are on PC, there are lots of mods which clear up the clunky issue of followers and their quirky inventory issues.
(EDIT: ^ Dabiene is correct -- dismissing a follower causes them to revert back to their default gear)