I think of it like this:
a) half from each parent (let x represent the Q's power):
1/2x + 1/2x = x
So q ends up with the same amount of power as each of his parents.
b) full potential of each parent:
x + x = 2x
But in this case he would have twice his parents' power.
Why not x * x = x^2? Or... dare I say it... Q Squared
Hah! Q squared!
Just as a child is a unique blend of two sets of DNA and can thus have abilities that his or her parents do not have, perhaps Q(junior) simply had some natural resistance to the Omega continuum. Perhaps that is what the Q feared, a change to the status quo, something new and different.