BlueJay and KA basically pointed out that what matters with opposed rolls is the spread. TaKe for example 60 vs. 40. If both players roll below 40 it is 50/50 who wins. If both players roll above 60 it is 50/50 who wins.
Point 1) Where the higher skill gets the advantage is the range between 40 and 60. If he rolls in that spread, he cannot lose the opposed tests.
Point 2) However, if the higher skill rolls above 60, that range belongs to the lower skilled character - he cannot lose if he rolls between 40 and 60 because of the rule: both fail lowest roll wins.
To compensate for the penalty to the higher skill due to halving take the case in Point 2 away from the lower skilled character. To do this use the following rule: When halving and both sides fail, highest roll wins.
So for normal opposed tests, both fail low roll wins. For Halved opposed tests both sides fail high roll wins.
The effect is that if the real skills involved were 120 and 80, halved to 60 and 40, the lower skilled character cannot win by rolling between 40 and 60 even if the higher skilled character fails.
Make sense?