So what is a clicker?
Without this key piece of information, the above won't be that relevant. A clicker is a term for someone who uses mouse-clicks to hit their abilities rather than keybinding them. There is an assumption made that people who are clicking their abilities are also using their keyboard to move. Their mouse is tied up with moving around the screen to hit abilities, and therefore only occasionally has the time to move their character. It's not necessarily true, but it seems a reasonable position.
Why does clicking get a bad reputation? Well, a couple of reasons. Firstly, it's slower. It is slower to move your mouse across your screen and hit different abilities than it is to move your hand across a keyboard. If you don't believe me, here's an experiment: head over to this keyboard site, and type a simple sentence by clicking the keys. Now try it with your keyboard. Unless there's something else at play, the latter should be faster. What's more, turn a full circle on the spot with your keyboard, and do the same with your mouse. One's a lot faster than the other.