It's entirely just you. The combat mechanics of the game work precisely as stated, although the mechanics themselves are a little controversial.
Personally, I see little problem with them. I rarely lose to a truly inferior unit, and sometimes cavalry *should* defeat infantry (world war I), sometimes warriors *should* fight off swordsmen.
And yes, true, occasionally a tank does get beaten by a spearman etc etc. Doesn't happen often, and it happens just as often in my favor as it does against me. (except of course, I tend to attack obsolete units more than the other way round).
Personally I'd make a few changes (longbowmen more expensive, better, english uu and everyone else gets crossbowmen for instance), however I do value playing the "real" game so I can compare with others and so I know the AI is working as intended.