Consider the play that we see in young animals. Chasing and catching is a rather universal form of play for all mammals, no matter their diets, when they are young.
I don't think it takes much to go from there to the necessity of catching to live. Chasing what moves can be applied to rolling nut, scurrying rabbit, bounding antelope...
As I said, I have no trouble with the concept that those animals which are carnivores now used to get all the protein and amino acids they needed from plant material, and I am thinking of roots and nuts in particular, with a helping of fruit now and then just because it is sweet!
I know you will disagree, but that is where I stand.