No you don't, and that's where the issue is. COH2 is based on random events a lot, you will never know who's going to win a mirror 1vs1 of same units (assuming equal conditions) and that can decide the whole game.
No, you do have an equal chance, but its decided by micro and RNG. The RNG issue is present all the time. If you follow that line of logic, then the whole game can always be decided on RNG. Assuming equal skill and balance, it doesn't matter whether it's a mirror or not, it's all about the dice.
Also, equal infantry fights only exist in a vacuum, like if you spawn two units into green cover. In a game, one guy has to engage the other and it is rare that cover and HP will be identical when both units stop moving.