**The first problem is one of engineering**. Assuming the reference to hover tanks refers to vehicles equipped with ducted air fans and a 'skirt' or similar the issue becomes one of weight vs mobility.

Any military tank fitting the classic definition has to be;

 A) Heavily armed - carrying a significant weapons payload of some type;
 
 B) Heavily armored/protected - equipped with armor and active protection systems capable of defending it from heavy weapons fire;
 
 C) Capable of maneuvering across varied terrain over an extended range. 

However with hovercraft you get a trade off. Specifically you generally get (C) at the expense of (A) & (B). This is because every kilo of weight you add in armor and weapons dramatically increases the size/power requirements of the lifting fans and fuel consumption of the vehicle. So for the cost of building a hovercraft with the armor and weapons of a main battle tank you could probably build a dozen more fuel/cost efficient 'normal' tanks

**Secondly you have the maneuverability issue**. Hovercraft are great at traveling over open/mixed terrain at high sped. And terrible at breaking, changing direction/cornering compared to  wheeled or tracked vehicles. **This is because their speed comes at the cost of traction**. (Which also makes them terrible platforms for firing cannons from BTW). And if you don't think traction is important (which it is) try taking a sharp cornet on an icy road at high speed.  Better yet, don't try, just trust me on this. Most of the time traction is a good thing!

For these reasons plus country on Earth has ever produced a heavily armored combat hovercraft

What hovercraft are good at is what the US used them for approaches to landing zones from the sea. Plus as transports for crossing soft/marshy/watered terrain. 

So you could create two types of military hovercraft;

(1) High speed/large volume military transports and;

(2) High speed, lightly armored missile/light cannon armed attack craft.

But no tanks.