The plot twist with Jon Snow was only revealed at the very end — he turned out to be a legitimate Targaryen. But let’s be honest — this significantly disrupts the logic of the Game of Thrones universe and even House of the Dragon. His survival was nothing short of a miracle, and here’s why.
A Look That Can’t Be Hidden
Jon Snow’s true parentage is one of the most shocking twists in Game of Thrones. In reality, he is not Ned’s illegitimate son but the rightful child of Lyanna Stark and Rhaegar Targaryen. However, this whole cover-up plan worked for one key reason: Jon didn’t look like a Targaryen. Dark hair, grey eyes — a perfectly Stark-like appearance.
Yet, throughout Game of Thrones, we are repeatedly told that true Targaryens are born with silver hair, and in the books, even violet eyes. House of the Dragon reinforces this idea by showing countless illegitimate children of Aegon, all of whom inherited their father’s white hair. Viserys married the dark-haired Alicent Hightower, yet all of their children were born fair-haired, as expected of Targaryens.

A Cruel Joke of Genetics
This issue is raised once again in Game of Thrones. Ned Stark realises that Robert Baratheon’s children are bastards purely due to genetics, proving that they have no rightful claim to the throne. Every viewer remembers how Cersei ordered the murder of all the king’s illegitimate children — all of whom, like him, had dark hair.
"The seed is strong" — This phrase ultimately sealed Ned Stark’s fate.
In the cases of Robert, Viserys, and Aegon, this rule holds true. Even Rhaenyra Targaryen’s story fits — the Strong seed proved dominant, and her illegitimate sons inherited their father’s features.

So why did Lyanna’s genes win in the case of Jon? It’s nothing short of a miracle, one that saved his life and allowed him to reach the series’ end.
Conclusion
Looking at all these facts, Jon Snow was simply lucky that Rhaegar Targaryen’s seed wasn’t as strong, and the child took after his mother. Otherwise, he would have been killed immediately, just like Rhaegar’s other children — or exiled from Winterfell to grow up in distant lands, like Daenerys.