Don't forget about shock absorption. If a tank were to take a fall, it would barely have any suspension to absorb the force of landing, the rest of the energy goes to something important (like the suspension or drive shaft) and breaks it. A mech would be able to absorb that force from landing a lot better (not 100% all the time, but a lot better than a tank. And tanks with legs like the Pupa/Shagohod of MGS would be considered mechs).
And on the note of terrain, I've tried explaining that, but he keeps going back to the "ground pressure" thing. Yes, mechs would sink somewhat in a lot of terrains, but when said terrain gets compressed enough, it is hard and stable enough to cross (hence why vehicles and living things leave tracks, they all sink somewhat).
And the mech can be anything from a Gundam, to a Armored Core, to a Chromehound, to a Heavy Object, to a Emporer class Titan, etc. ANd on the note of technology, I do agree with bryon on that, techs that will advance mechs will also advance tanks and current types of vehicles. However, we simply don't know how the warfare of the future will be handled. We once fought in large battlelines charging with swords/spears, then we had battlelines with ranged weapons sitting at range blasting at each other, then we had skirmish lines picking off the enemy while behind cover, then trenches, then blitzkrieg, etc etc, all the way to our current tactics. Who knows how we evolve warfare in the future, you never know, we could find that mechs are more potent than you believe or that they are a terrible weapon platform.