You can only take only one reaction during a combat round though. So if you cast a fireball, an enemy mage counters you, and you counter his counter, that is the end of reactions for this round for these two characters.
Ok but this then means whoever goes first has a huge advantage. They get to both act and counter, whereas the target of your act only gets to counter and does not get an act of their own.
Well, casting counter spell costs you a 3rd level slot, that is not exactly free. Since you can react only once, the caster casting the first spell (ex fireball) will have the final word on the double counter sequence. But it will have cost him dearly to pass his spell.
You also need to consider that your reaction only recharge at the beginning of your own turn.
Mage A turn:
Mage A cast a fireball, Mage B counterspell, Mage A counterspell the counterspell.
Orc attack Mage A. Mage A can't use shield to protect itself, as its already used to counterspell.
Orc move away, Mage A can't opportunity attack as its already used, ...
Mage B turn:
Mage B cast lightning bolt, Mage A can't counterspell, reaction already used too...
You can imagine how using your reaction, being first or last in initiative order, is not that of an easy thinking !