Ok, settle in, because this is going to get byzantine.

The background of this is that Cregan Stark was a serial monogamist with a gift for children living to adulthood. 

• With his first wife Anna Norrey (who must have died young for reasons that will become clear in a second), Cregan had his firstborn son Rickon, who married Jeyne Manderly and had two daughters before dying outside Sunspear in the armies of Daeron the Young Dragon. 

• Cregan married a second time to Alysanne Blackwood after the Dance of the Dragons, and had four daughters (doesn’t seem like any of them had issue). 

• He then got married again to his cousin Lynara Stark (although where she came from is a bit unclear, but it must have been back a few generations at least since she wasn’t the descendant of his uncle and his grandfather only had two sons), and had four sons with her. 

This caused something of a dynastic issue, because Rickon’s daughters Serena and Sansa had a claim that arguably would supersede those of his living sons and at least Serena was married into the Umbers so she had political backing. Meanwhile his living sons also had significant political marriages: Jonnel (the oldest) was married into the Ryswells, and Brandon (the youngest) was was married into the Karstarks (but sleeping with a highborn crannoglady from House Fenn). 

As the Peter O’Toole in the Lion in Winter that he was, Cregan dealt with the situation by marrying his relatives to one another. Serena Stark’s Umber husband died, so that let him marry her to Edric (his second-oldest), and Sansa was married to Jonnel, whose Ryswell wife had also conveniently passed away. Problem solved, right?

Except that Jonnel died without issue (which leaves Sansa a loose end), then Edric had twin sons and two daughters (who married into the Umbers and Cerwyns, and had issue), except that Winterfell didn’t pass to any of them (the sons may or may not have been alive), instead it passed to Barth Blacksword (the third-oldest) and from him to Brandon. I don’t imagine this went over well with Edric’s wife, who had now been passed over twice and who had the Umbers and Cerwyns on her side and the Manderlys (although they might have been temporarily peeled off when the Manderlys married Rodwell Stark), but it’s not like the Karstarks were about to step aside when they had an adult male Stark with two half-Karstark sons waiting to inherit. 

Beron was the youngest of those two sons, and was mortally wounded fighting Dagon Greyjoy’s Ironborn, leaving behind five sons who were probably around Egg’s age at the time. However, alongside Lorra Royce, Beron’s widow, you probably also had Arrana Stark and Aregelle Stark (the daughers of Edric and Serena) both of whom had issue and a claim that was undeniably better in everything but proximity, you might have had Lonny Snow or the Blackwood daughters still kicking around. 

So you have a nasty combination of competing claims and competing power blocs.