11/03/2021
Imagine DNA as a pack of 52 cards. Everyone has 52 cards, and everyone gets half of these from Mom and half from Dad. That means out of the 52 cards your Mom holds, she’s given you a copy of half of those in her hand. But, this is a shuffled pack. Each time a new baby is born, Mom and Dad both re-shuffle their cards before handing them out.
Your maternal great-great-grandmother, "Mary" had lots of children and multiple grand-children. Amongst her cards she had the Ace of Spades, the Queen of Clubs and the King of Hearts. Through the generations your Mom ended up inheriting the Ace and the Queen. But she did not inherit the King.
Now, when your Mom took her cards, shuffled them and gave you half – you happened to inherit the Ace of Spades. This means you will match with any of Mary’s other descendants that also inherited the Ace of Spades.
When your Mom had your brother she shuffled her cards and gave him half. He got lots of the same cards as you, but he didn’t get the Ace of Spades. Instead, he inherited the Queen of Clubs. Now he has matches with the descendants that inherited this card from Mary. Matches that you don’t have – because you didn’t inherit the Queen.
You have a DNA match descended from Mary that matches both you and your brother. That’s because this match inherited both the Ace of Spades AND the Queen of Clubs.
There are other cousins you’ve identified through paper research but neither you nor your brother are genetically matched to them. That’s because they inherited (for example) the King. A card that did not pass down to your Mom and therefore couldn’t pass down to you.
The random nature of DNA is why asking as many family members as possible to take DNA tests can be so helpful. Imagine if one of Mary’s descendants took a DNA test and had the King. If she shared her DNA matches with you, you’d have a whole new set of Mary’s descendants to explore