Since the velocity of rotational motion of Earth equals orbital velocity of the satellite, they are relatively at rest to each other. If so the satellite should be at constant position above the Earth's surface. How can it revolve if it moves with the Earth?
Look at the Earth from the Moon. Block out the Earth with a disc so you won't be distracted by the Earth's rotation. Now you will see the satellites move round the Earth once every 24 hours; the same as we observe Venus orbiting the Sun.
The fact that the Earth is turning is nothing to do with the satellite's orbit around the Earth.
Basic stuff first: Newtons cannonball
You're no doubt familiar with how things arc when thrown. The harder you throw something, the shallower its ark. If you were to throw (or shoot) something with extremely high velocity, its 'arc' would match the curvature of the earth. Enter, newtons cannonball.
If the arc of your fall matches the curvature of the earth, then congratulations! You've reached orbit.... Well, Kinda. There's nothing special about the curvature of the earth, it's all about its gravitational field. The exact same orbit would work just as well around a pea-sized black hole with the earths mass, or a world-sized spaceship, or a earth-mass pyramid. But most massive things tend to collapse into a sphere, so 'matching the curvature' is just a good description, nothing more.
Point is, the spin speed or even shape of the planet is irrelevant, all that matters is its mass. Which brings me to point two.
Geostationary orbit isn't about the orbit at all. If earths day-night cycle was a month long, the moon would be in geostationary orbit. If it were 90 minutes, the ISS would instead (And the planet would disintegrate but... One thing at a time.) All geostationary orbit means is that the orbit takes 24 hours to complete - and as a happy coincidence that matches the time of our day. Since it takes us both 24 hours to go around the center of earth once, a geostationary satellite seems to hang directly above us, in the same way that a car driving next to you on the highway is car-o-stationary.
Welcome to the world of coordinate systems/reference frames! When you say "revolve around the earth" you have made an ambiguous statement because the next question would be "relative to what coordinate system?" From your argument we could say that the earth isn't rotating because one point on the earth isn't moving relative to some other point on the earth.
Let's consider a coordinate system with its center at your house and the $x$ axis pointed continually at the star Sirius. $y$ is fixed parallel to the rotational axis of the earth. In that coordinate system, the $x$ position of the satellite is changing. The location of the satellite oscillates around the center of the coordinate system, slightly non-circularly, returning to its starting point once every 24+- hours. The center of the earth has also revolved around this coordinate system.
If you choose a coordinate system centered at the moon with the $x$ axis pointed constantly toward Mars, there would be a complicated description of positions.
For geosynchronous satellites, they must revolve about the earth's "center" (it's a bit more complicated that the middle of a sphere because of non-uniformities in earth's structure) at the same rate that the surface of the earth is rotating about its own center. Both satellite and earth spin at the same rate relative to some coordinate system which involves a third celestial object.