A conservative force is naturally the vector gradient of a given scalar field . I don't know why the convention to put the negative sign in front of the gradient operator. 
Or is this just a misconception some of my professors had?

The gradient of 1/r is automatically in the negative r direction, so saying the force field is negative gradient is straight up wrong, if it were true the Earth would explode..

Edit:
It was brought to my attention that physicists like to define energies of classical systems to be negative. That answers the question of why they would take the negative gradient..

But really it just rises more questions than answers..
I thaught energy would almost always assumed to be non negative. 
Also energy is simply the hamiltonian of the lagrangian system.. so why even bother about some sign conventions in the definition of energy?