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In this alternate world, demigods were human beings which gained divinity from a divine parent. A male deity would knock up a mortal woman, who would carry the child to term. This demigod would share the divine essence of the divine parent, but would be sustained by a mortal womb and fed mortal nutrients. While they would be powerful, they had limitations and were not unkillable. This makes sense in context because half of their makeup would be mortal.

The reverse should be true if the demigod's mother was a goddess. That child would be sustained by a divine essence in a much more direct way due to it literally growing inside a deity. Such resulting beings should be much more powerful and be as immortal as their mother. However, this is not the case. Demigods born to goddesses appear to be just as vulnerable as their mortal counterparts. For example, Achilles, a hero from Greek myth, was born to a goddess and a mortal man, but was bumped off in the most idiotic way by being shot in the foot with an arrow.

I need to justify this contradiction for this world? How could I explain this?

In the animal world, babies born to parents who are very different from each other have some characteristics that may be different at birth (size usually starts off to match the mother, so a too-large baby doesn't kill its mother during or even before birth) but then even out (size generally does) and some characteristics that tend to be different depending on which parent came from which group.

For example:

Many foals are born with oddly bowed legs. This is called ‘windswept’
and is common to large foals born to smaller mares. Because their
ligaments and tendons are immature, they may also walk with their
fetlocks almost touching the ground. Within a few days, as the foal
becomes stronger, the legs should show signs of straightening up. (emphasis mine, ref)

In this case, the animal has an adaptive feature because of a mother not matching the baby. But it's temporary.

Then there are hinnies and mules. A mule is the product of a horse mother and donkey father. A hinny has a horse father and donkey mother. Mules are, as a general rule, more intelligent and vigorous than hinnies, and also a bit larger. There is a bit of controversy about the details though.

In no way does a child only follow the mother. Even if the child has the mother's culture/experiences and food.

In your case, your demigods are always going to be demi. Half. They will never be full gods and will never have all the characteristics and powers of a full god. Infancy is a very important time for all living creatures and there could certainly be differences in your demigods based on who raises them and where, the food they get, and so on. There can also be differences based on their gestation periods. But their genes will be half and half.

If you look at demigods like Achilles, he was born completely mortal and as vulnerable as any human (perhaps with some extra abilities). His protective powers came from being dipped as a baby into the River Styx. His one weakness (his Achilles heel) was the part of his body that didn't contact the water (because his mother had to hold on to him somehow).

If you choose for a demigod to be mortal (though perhaps longer-lived and harder to kill), then they are. If a child born to a human mother and divine father is mortal, then it follows that a child born to a divine mother and human father would be too. That to me makes more sense than giving a only one of those groups immortality.

I don't see a contradiction, unless you believe Mother's milk has some special property that we need to get around. If the goddess is lactating ambrosia, we have a problem. But if she's just lactating milk, then the child would have the same limitations as one sired by a god. An identical argument could easily be made with gestation. Basically, if both chromosomes aren't divine, what you get is a mortal demigod — period.

(where this really gets fun is if the demigod mates with a god. If we use the same rules for, say, eye and hair color, you now have a 25% chance of bearing a pure mortal... oh, yeah!)

So the first thing you have to take into consideration is that the peoples who believed in these gods and demi-gods they followed it blindly. The odds that they even thought of this would be very slim. To them all they know is a god or goddess who has a child with a mortal becomes the parent of a non immortal demigod. The reason this worked back then, was because it WAS the way to believe. Anything contradictory was looked down on.

Now as far as justifying it... You may have to think of the godliness coming from the creation of a soul. Regardless the nutrients that were fed, the soul was created at conception. This would make it so that regardless the combination of parents, if a god's and a mortal's soul creating juices were combined, it creates a non immortal soul with godlike powers. Since gods are pretty well considered magical, it would stand to reason that their powers come from their souls.