I agree that the result is the same but the implications are different.
In many other cases it could happen that an infantry unit attacking another infantry unit gets counter charged by cavalry and depending of the order of the combat it could mean that at some point you could have a combat where the infantry unit that charged finds itself finally fighting only the cavalry.
Now, reading carefully in page 54 it warns that it is dangerous for infantry to charge when cavalry could counter charge them ( because they will not be in square ) and in the example in page 58 it specifically says clearly "( Even had they not been in contact with two enemies, infantry not in square would be halved against cavalry )"
This would indicate that the half dice for infantry not in square vs cavalry was still meant to apply when the infantry is charging but is itself countercharged.
What I am trying to understand is if this is the original intention of the rules as explained in these statements in the two examples ( ie that infantry would ALWAYS be at half dice when fighting cav not in square ) or if the examples should be ignored to preserve the integrity of the rules as written.
I am not trying to be stubborn, but is is not difficult to imagine the case were a unit of infantry charges another inf unit. It is itself coutnercharged by cav, the combat between the inf units is fought and despite the odds the charging unit wins and the next combat is the charging infantry against the countercharging cav, and now the "touching two enemies" rule does not apply and as per our current interpretation the inf not in square is not applied.
But the other player might correctly point out to the quote I posted above saying that it should apply.
thanks
Francisco