Towards the end of Parshat Vayechi, Yaakov blesses each of his sons before his death. Each son receives a different bracha dependent on his individual character. For example, the blessing given to Yehudah used the symbolism of a lion. Since the lion is strong, powerful, and dominant, Yaakov blessed Yehudah that he, too, would have those qualities. Another example is the blessing given to Dan, which used the representation of a snake. Just as a snake is powerful because it is sly and attacks people from behind, so too Dan will demonstrate these traits.
The Radak explains that a snake may even be more powerful than a lion, as a snake attacks its prey alone, whereas the lion virtually always attacks in packs.
The question may then be asked why Yehudah is the most powerful and dominant, instead of Dan? After all, Dan is compared to a snake and a snake, very powerful, and maybe even more powerful than a lion, Yehudah’s animal!
In order to answer this question, one has to look at the characteristics of both Yehudah and Dan. A look at Yehudah and his descendants reveals that he not only starts off as powerful, but maintains his power. David, for example, was a great king and a heroic leader who never lost these qualities; he always managed to fight off his enemies and be a fair king. As Rav Saadia Gaon says, Yehudah will never lose the authority he had over everyone else.
Dan, on the other hand, does not always keep his power, but rather loses it in the end. Dan is like the snake in the Bereshit story, which at first had great powers of language and slyness, and was able to persuade Chava to eat from Etz Hadaat. However, in the end, he lost his power and was punished by only being able to eat dirt. Shimshon, a member of the tribe of Dan, was very strong and dominant in the beginning. He was able to tear apart a lion and he was a Nazir, making him very close to Hashem. Nevertheless, he lost his dominance in the end, and gave way to weakness. Overall, Dan, unlike Yehudah, cannot maintain strength, and is therefore less worthy of the Malchut.
It now makes sense that Yaakov gave Yehudah the blessing that he will be dominant and rule over others, instead of giving it to Dan. Yehudah always exhibits the characteristic of being able to maintain his dominance, whereas Dan cannot. However, Dan was still blessed by Yaakov that he would have power, only not with the same magnitude and authority as Yehudah.