Because it is the observer who is rotating, if the observer doesn't take that into consideration, then it will appear the whole world is rotating but not the observer ... think of a rock-fight on a merry-go-round, if you throw straight at your enemy, she will be rotated out of the way before the rock gets there ... everyone outside the merry-go-round will see the rock fly straight ... the difference is the rock-thrower is herself rotating, even though she believes she is stationary ...
The problem is we have to be free of all forces acting on us in order to observe the forces around us ... and this is called the inertial frame-of-reference ... except that standing still on the Earth's surface, we're under the influence of gravity, and thus this "standing still" is non-inertial and we won't observe any forces in their true form ... we like to say "the Sun moves across the sky", but reality is is we who are moving underneath the Sun ...
Therefore ... to observe the Coriolis effect, we ourselves must be rotating, like standing on the Earth's surface ... if we're out in space such that the background stars are stationary, and we're looking down on the rotating Earth, we will NOT see any Coriolis effect ... rocks and cannonballs fly straight ... yet cyclones are obvious ... thus there must be a different explanation to cyclonic motion which must rely on real forces, the pressure force and convection ...
Note also that the pressure force is of equal magnitude but opposite direction from the Coriolis effect ... so the Coriolis effect is pointed the wrong way ... and in vector math, that's important ...