okay from what i have noticed ap is alot easyer to get high then attack damage

why is this is attack damage more useful

Because most skills have AP ratios and cant be cast 2 times a second. I've gotten over 1000 ap multiple times before, if a carry were to get 1000AD, that would be so broken.

AP ratios are usually less than 1.0 and have cooldowns around 10 seconds before CDR. All champions come with a built in 1.0 AD ratio attack that can go all the way down to 0.4 cooldown. That's why. You can apply your AD much more frequently than you can apply your AP.

Most casters can only throw their spells every few seconds at best, most usually have long cooldowns somewhere.

Right clicking the enemy doesn't have a cooldown, plus the attacks can crit unlike spells. Thus, AP is easier to gain as a stat. (keep in mind too, that most spells have a ratio around .8)

Nature of the game, as others have explained. To simplify it a bit:

AP Carrys are generally "Burst" damage. They unload a lot of damage fast, then they must wait for cooldowns before they can unload another burst.

AD Carrys are generally "sustained" damage. They lock onto a target and maintain a constant flow of steady damage. It doesn't (always) chunk away huge portions of HP or blow someone up like an AP carry's combo will do... but it will slice away several slivers of HP for as long as you can stay in range and not die.

it is the reasons stated above that shows why mages are the weakest class right now, they are still viable but very weak. MR and Armour despite working the same way have very different effectiveness to each type of damage, armour only slows down a dps champ so can mostly be ignored untill you get around 250.

mages on the other hand need to kill their target outright otherwise they will likely die before next rotation as the target has plenty of time to just healup via lifesteal or escape, 100 MR halves all their damage before pen and its not hard to get 200 at which point mages cant drop you below 100 and cant kill anyone. for a dps on the other hand it just means they will need 7 seconds to kill you rather than 4