How to make your followers craft

Followers are generally given a set of skills that will improve, regardless of what you equip them with. These will improve with level, but nothing else will. Faendal is always going to do better with bows than with a greatsword, for example.

To this end, the official strategy guide states:

• Sven's skills are alchemy, enchanting, smithing, and archery
• Lydia's skills are in one-handed, heavy armor, archery, and block; not sneak

It's not clear where the rumor that Lydia would make an excellent thief started: UESP mentions she has the sneak skill on the list of followers (I suspect that's where Wikia pulled the information), but her wiki page clearly marks her as a warrior (the correct designation). Nothing about her says "stealthy": she starts with a sword and board and tells you over and over that she's there to protect you.

While the official strategy guide does list what each follower's skill is, with the exception of Lydia, UESP's version matches up with the strategy guide, so it should be pretty accurate to determine what skills your follower has.

But if you wanted to do it without consulting a guide or a wiki, it's generally common sense and usually based on what equipment they come with. Lydia comes with a sword and shield, so her skills are one-handed and block; Faedrun comes with a bow, so one of his skills is archery; and so on.

SOLUTION!!!

I can confirm that I too had this issue on the PS3. No matter what I did I could not get above 22% in my items with same information you have given.

I went into game data on the ps3 menu and deleted the game data and the game update for Skyrim. Launched the game and let it patch and reinstall the game. I then went straight to an enchanting table and with no enchanting gear I could create +25% alchemy gear using Grand Gems alone.... I edited a section on Wiki about bugs and stated that I confirmed a solution to this problem.