I don't know if anyone asked these questions however:
1) was the city he was attacking on a hill?
2) I doubt it, since the AI was on chieftan, but was their a wall around the city?
3) What was the population of the city?
4) Was there a river on one side of the city across which this person was attacking the AI?
Even with a warrior, if #1, 3 and 4 were "yes", 7, and "yes" thats could bring the warrior up to 3.5 defense, 4 if the AI rounds up (dunno if it does that, I forget). Then there is the defense bonus the other unit gets for being on its own territory, and the fact that it was fortified.
If you aren't careful and don't analyze the people you are attacking you could easily find yourself facing a warrior with an 8 defense and watching it kill your cavalry.
I will say it once again, the AI DOES NOT CHEAT. This is about design. Computers don't cheat (I hear it all the time from my son thinking the computer is somehow out to beat him for personal reasons). It just doesn't happen that way. The AI is designed to know aspects of the map and where your units are and to analyze both defensive and offensive positions.
Civ1 and 2 were more production intensive. If you could out produce your enemies you'd win the game. Civ3 is more unit intensive. Combats are far more complex, and often lend themselves to being more about chance due to the way probability works. I find in a war I'm waging now the computer is finding ways to throw their MIs against my MIs and even though mine are fortified in cities of population 15 it is taking only one of their MIs to kill one of mine. Its insane, but its bad luck to.
In civ2 the unit hp based on the age the unit was in was good, but it there was very little luck to it, and you never saw a battleship lose very many battles.
Yes, there is only a 4% chance that the spearman I'm attacking with my MA is going to lose a hp in one round, but every so often it happens. In order to make the game more challenging they had to reintroduce some of the randomness of the game.
I apologize for your losses, but you have to realize its a game. You also have to realize that when you go off on a rant like this you sound like you are exaggerating things. If you want us to take this seriously, make your argument clearly and concisely with screenshots so we can see what you are seeing.