Your contractor was right.

I don't know what the coating is, but imagine it is epoxy, cementitious or a paint variant. Where the coating has peeled, do a water droplet test on the exposed concrete. If the water drops absorb within 10 minutes you are golden.

3 ways to go with this:
Home Depot scarifier rental (it weights > 200 lbs); edges & stairs are challenging
SDS-Max drill with chisel bit in hammer-only mode (probably also a rental)
angle grinder with a diamond cup off ebay & wet grind; probably The scarifier will be fastest & the best choice if the coating is elastic (it would gum up a diamond cup). The angle grinder works out cheapest if it takes more than 1 day. I would avoid the chisel on thin coatings.

Just as an aside, any chemical product that you use to try & break the bond of cement to coating will also weaken any future product's bond: you can't totally neutralize the solvent.