How do you time your smite?
Do you watch the monster's health, see it go below smite value, then press smite? This is the naive way to smite and is decent for general purposes, but it can be beaten regularly by people who put more thought into it.
Human reaction time to visual stimuli is ~0.25 seconds or ~250 milliseconds, and your ping probably adds 50+ms on top of that, and literal reaction time doesn't improve very much with practice so the best your smite timing will get with this strategy will probably leave a 250-300ms window in which the mob can be stolen.
To actually improve and reduce this window, you need to have an idea of how much damage is being dealt to the monster and time your smite to go off during that instant. People are capable of timing to a much shorter window than your reaction time, consider a game like DDR where almost anyone can achieve long strings of "Perfect" on moderate and lower difficulties when every single "Perfect" requires accurate timing within two frames, or about 33ms. Of course, DDR has a steady rhythm, musical cues, and a fixed track every time while killing an epic monster is going to be different every time.
Warwick as a champion also has his Q as an ability that forces you into this timing game by being a very large nuke against epic monsters (the % health damage component alone can easily be over 300 damage) by bringing the monster down into smite range with a timing he is probably more used to than you are.
