What should be called a force? Physicists say that there are four fundamental forces in the universe: gravity, electromagnetic, and the other two. But when the gravitational phenomena were explained by the General theory of relativity, the belief that gravity is a force becomes weak. So the fundamental question is that if one day someone explained the phenomena associated with the other forces in a similar way as gravity, would they then still be called forces or would they be instead called, for example, curvature in some "other thing"?
 A: It's really doesn't matter what you really call them (more or less depending on the area).
The gravitational force is attributed to the curvature of spacetime, described by Einstein's general theory of relativity. The other three are discrete quantum fields, and their interactions are mediated by elementary particles described by the Standard Model of particle physics.
But we still call them forces in elementary courses. If you go into a higher course, like QFT, we regard these as fields.
In Newtonian mechanics, Even now we consider gravity as force and this work very well.
A: As existing theories are replaced by new theories the existing words are redefined.
Example:
During the time that Caloric theory was assumed to be true the word 'heat' was understood as 'amount of Caloric'
Later Caloric theory was replaced by the kinetic theory of heat. Physicists did not stop using the word 'heat'. Instead 'heat' was redefined: kinetic energy of molecules and atoms.
The newtonian definition of 'force' is: that which causes acceleration with respect to the local inertial coordinate system.
So: upon moving from  newtonian dynamics to GR we need to redefine how the word 'force' is to be understood.
One way is to define 'force' as the derivative over distance of potential energy. We all agree that gravitational potential energy is an indispensible concept. As a comet moves from the outer reaches of the solar system to the inner planets gravitational potential energy is converted to kinetic energy.
If it is agreed that there is such a thing as gravitational potential energy then it follows that gravity is a force.

When people say: "Gravity is not a force" then what they are actually saying is:
If we move to general relativity, but at the same time we keep the newtonian definition of force, then gravity is not a force.
