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For those of you who don't know, Attack move click is essentially the smart cast version of attack move. If you bind it to A, when pressing A you attack whatever is in front of you simply by pressing a instead of needing to press A and then click (which is what is enabled by default). So Attack Move Click is very beneficial for AD carries and kiting, especially once they start to have a significant amount of attack speed.
However, when you enable attack move click, there is an annoying bug. If you are typing to your team and ever type the letter A (or whatever you bind it to), you will attack move to wherever you mouse is. This can be a problem in many circumstances. For example, while recalling, if you are typing to your team and press 'A', your recall will be cancelled as your champion starts moving to your cursor.