As far as I know...
There is no universally accepted answer regarding what causes gravity. Though we understand the effects of gravity, exactly what causes it is not yet exactly known to the scientific community, let alone us folks.
Gravity is NOT affected by the rotation of the earth, as far as I know. What your friend might be saying is that there are claims that gravity is due to the rotation of the galaxy. However, arguing on these things are useless as they involve quite advanced physics, which only a few people in the world can understand.
What grade are you in? You will learn about Newton's Theorem of Gravitation in your A/L s if you do physics.
Newton says that any two bodies are attracted to each other, and the force of attraction is directly proportional to the product of the masses of the two objects and inversely proportional to the distance between them. Rotation speed does not come into the equation.