Jon Snow has the strongest claim to the Iron throne

Fair enough. Given medieval law the right of succession is tricky at best. Since we are not saying Jon has claim to Highgarden, or Stormsend- and instead the Iron Throne, we must base his right to rule off his connection to the Tararyens. The Targaryens are the only Royal Blood line that has the right to rule the Iron Throne by law. Robert's claim to the Throne was that his line had Targayens in it. Stannis's claim is predicated off the fact that Robert's children are not true-born, his own Targaryen blood, and that there are no other living Targaryens better related to Aryes- That is a weak claim at best Laws of succession in this time are as follows -When the king dies power passes to family in this order- 1. Heirs 2. Children of heir 3. Brothers 4. Daughters 5. Other relatives It should be noted that other relatives would often assume power before daughters, it was case to case really. So we have the law of succession in GOT 1. Raegar Targaryen (dead) 2. Jon Snow 3. Viserys (dead) 4. Daenerys 5. Stannis, and half of the seven kingdoms. It's clear whos claim is the strongest. The issue with Jon's succession is that he may or may not be a Bastard. This is all speculative at this point as we do not know is Lyanna was kidnapped or instead Eloped. Even if Jon is a bastard his claim still outstrips Danny's and Stannis's. - You see Stannis is a Baratheon, through and through. Thought he may have some distant and dead Targaryen relatives he is not a Targaryen himself. In Feudal societies noble families intermingled a lot. They all shared the same decedents and had grandmothers and grandfathers from other noble houses. It didn't matter though, what mattered was you name. It didn't matter if your great great grandmother was a York if you were a Lancaster. It was so common to have relatives belonging to different houses that if you based succession of your Grandmothers last name, every person would have a claim to the throne. So only if EVERY other member of the ruling family was dead you would you see power pass to nobles based on dead relatives- but only in that circumstance would it happen. It happened to Robert because he defeated the Targaryens and killed them all. It happened because to everyone's knowledge there were not Targaryens left - Danny is a woman. Doesn't matter if she is true-born, doesn't matter if her bloodline is pure. She was never made the Heir and worse yet is a WOMAN. Woman almost never inherited power because it weakened kingdoms. It is known that Kings rule, not Queens. So if you gave power to a Woman and she married a man from another country, you would have a foreign man now ruling as king. It would be like a Korean CEO becoming the American President. Moreover the woman takes the mans last name so your namesake, and your bloodline would die. Even though your dynasties blood would still flow through the veins of the following heir, he would have his fathers last name. This means the end of your dynasty and that is bad for business. Therefore woman were at the very bottom of the inheritance list, and it makes sense why. Occasional power would pass to sisters or daughters, but only if that sister or daughter was shrewd enough to take power and respected enough to maintain it. And that only happened if no other males existed to claim the throne. And still this was not happen by law, it would only happen in that given daughter had to will to take the power herself.