Why is it that, mages for example, do not want their "armor rating" to go up? Like right now, I have an armor rating of 0 because I'm a mage and I'm wearing all clothing. But I want to wear this "Diadem of the Savant"(Looks like a circlet) which makes all spells cost less magicka.

Only thing is, it's armor. +8 armor. I thought back to reading this forum and remembering that If I'm a pure mage I shouldn't wear armor. Why?

I beleive it has to do with one of the perks, if you are wearing armor it doesn't count even if you picked it. I hope someone else has a clearer answer.

edit:

http://www.uesp.net/wiki/Skyrim:Mage_Armor#Mage_Armor This is a good page to read.

One of the alteration (?) perks boosts your alteration spell armour rating significantly if you aren't wearing ANY armour. I think it's double or triple or both...not sure because I don't use it.

Aside from that, it's just personal choice....some people like to be tanks, some people like to be meat sacks.

This is not true. A mage can wear heavy armor and it does not hurt the spell casting.

Once you join the College of Winterhold, You will be given a better Circlet (Enchantment-wise) that is not Armor and does not affect Alteration Shield Spell Perks. If you wear the Diadem of the Savant, and you choose to run the Light Armor route, then the Diadem is useful for achieving the Light Armor Perks, the enchantment helps a character who uses Melee/Spellcraft, but it is a pointless enchantment at higher levels for a pure Mage because your character will be building a very large Magicka pool.

I have a pure destr mage in light armor, and a conjurer mage in heavy armor.

Don't see anything wrong with either one - whatever you prefer.