TC garrison and boar/deer hotkey

I’ve been practicing boar/deer killing and have some questions on how to do it faster with fewer mistakes. I noticed that when deer pushing, most players garrison some vills and then ungarrison them from TC to kill it. Why not just grab the vills and kill the deer directly, which have a lot fewer actions/hot keys to press? If garrison/ungarrison is better, what are the exact hot key sequence do you press? Is it like, 1) Grab vills, 2) garrison hot key, 3) gathering point hot key 4) left click the deer, 5) ungarrison hot key? In this case since there seem to be five actions, how can you do them so quickly? Or maybe there is a faster way with fewer steps?

Also, when using TC to kill boar, you 1) select vills, 2) press the garrison hot key, 3) left click the TC 4) press the gathering point hot key, and 5) left click and set it at the boar and see click? 6) Right click to shoot at the boar 7) ungarrison hot key. Is this correct? In step 5 do you press right click instead?