Level 2 enchanted book doesn't enchant level 3 enchanted item

Why do you want to have a lower protection level on your armour than it already has?

The video is quite blurry but it appears you don't have enough XP to do that anyway

Robbage yes i know but when I grabbed a different item off of the anvil it still had the same level of protection. It had level 1 on it but when I added the protection 2 it only went up 1 level instead of 2. Sometimes it will enchant by 1 level or not at all

And i don't want to have a lower level of protection, I had protection 3, and if I add protection 2 it should be protection 5.

First off, maximum level of protection is 4. Second, you need two of the same enchantment level to go up a level (so you would need an additional protection III book to make the leggings protection IV.

Ok so if I had a level 3 item and added a level 2 book would it go to level four?

Well later today I will test a level 2 book combining with another to see if that works

no you need level III

No it should go to level 4 since I will combine a level 2 book with another level 2 book

It's not addictive, you cannot combine different levels of books to achieve a product of the levels.

Example:
Correct: Protection II + Protection II = Protection III
Incorrect: Protection II + Protection II = Protection IV

Each combination of the same enchantment level creates the next level enchantment.

I + I = II
II + II = III
III + III = IV