I think it can be cast multiple times on the one city.  Check your unrest - you need to cast Dispel Enchantment one time on that city for every Antipathy curse there is on that city.

Also it seems kind of silly that dispel enchantment dispels a random spell. Say that I have 2 enchantments on my city + antipathy. To dispel antipathy I have to remove the 2 enchantments and cast dispel enchantment - then cast the 2 enchantments on my city again, or I can roll the dice and cast dispel enchantment 1-3 times to get rid of antipathy. Either way, it is very expensive in mana onless I am Lucky with the dice.

Have I misunderstood something or is that the way it just works?

Ok, thank you, that makes more sense

Somebody should point out how it is against every rule of good game design to have the counters cost a whole lot more than what they are countering.

Keep in mind that antipathy costs your enemy 30 mana +1 per turn to cast.  Dispel costs you 90 mana to cast.  It's seldom worth the exchange rate just for 10% unrest, unless the former enemy that cast it on you is now your bosom buddy.  My favorite method for purging the effect is to kill the caster and all of his people.  No civ = no spells.