Let's use you as the example. Why will your hypothetical child have only 50% of your genes?
There is a process that your cells go through to multiply and grow. However, your reproductive cells are special, they undergo a different, but similar, process.
The cells in your body copy their DNA, then split into 2 identical daughter cells. Each cell will have 100% of the DNA of the original parent cell.
In the reproductive cells, sperm and eggs, you will see a 2 step process.
Step 1: Sperm/egg will copy their DNA as normal, but an important process occurs that doesn't occur in normal cells. During this time, your mom and dad DNA copies will exchange genes. In other words, because you obtain one DNA strand from your dad, and one from your mom, they are similar enough to get mixed up during this Step 1 process.
To clarify, you have a DNA from dad for black hair and big feet. You also have one from mom for red hair and small feet. Since these both deal with hair color and feet size, they can become jumbled, leaving you with a DNA strand for black hair and small feet, which you may deliver to your hypothetical child.
Once this mixing of genes is done, the cell divides, leaving you with two daughter cells, but with new genetic information. Technically, these cells are no longer "you".
Step 2: At this point your two new daughter cells still contain 100% of the amount of DNA in the original cell (because cell division involves doubling, then dividing into 2).
short answer/tldr
Cells that will become sperm/eggs divide twice, rather than once (like normal body cells) which will leave them will half the normal amount of DNA. This process can go wrong and give you more than half, but these babies are either never born, or they are born with lifelong defects like Down's Syndrome.