If I share 50% DNA with both my parents, why do I look so much more like one of them?
This is more interesting than it sounds - let me explain why.
Yes, you got 50% of your DNA from each parent. But "look like" is determined by a small subset of your DNA - maybe a few hundred variants that influence visible facial features, skin tone, hair, eye shape. Which half of each parent's DNA you got is random, and the random draw might have given you most of the appearance-relevant variants from one side.
So you can be 50/50 by total DNA and 80/20 by visible-trait DNA. That's not a contradiction. It's exactly what the maths predicts will happen sometimes.
There's also a less obvious factor: dominant versus recessive alleles. If your mother contributed a dominant variant for, say, a strong jawline, and your father contributed a recessive one, you'll show your mother's jawline even though you carry both versions in your DNA. Your kids could still inherit the recessive one and look more like their grandfather.
So: 50/50 in DNA. Highly variable in appearance. Both true.
Great question, this comes up a lot when families bring babies in.
To add to Arjun's answer: people sometimes notice that a child looks like one parent for a few years and then "switches" to looking like the other parent. This is also real. The genes for facial structure express themselves at different rates as the face grows - toddler features are dominated by certain variants, adolescent features by others, and adult features by yet others.
The same child, photographed at 3, 13, and 30, can convincingly look like a different parent in each photo.