I honestly think that Blackbeard is Rocks/Rox’s son. Rox’s era ended around 40 years ago. Blackbeard is 40.
Whitebeard was a part of Rox’s crew and probably saw him as a father figure. I don’t think that it’s a coincidence that Blackbeard joined Whitebeard’s crew, seeing as how he saw everyone as a son. We don’t know if Rox shared this sentiment, but if so, it could one another as to why Whitebeard desired a family. I also don’t think Teach would join Whitebeard without having some context as to who he was.
We don’t know Roger’s relationship with Rox, but we do know that Garp took down Rox.
If you stick with the generational inheritance, Luffy is the one who’s gonna take down Blackbeard. If Roger did run into Rox, he may have lost a fight to him in a similar fashion of how Ace lost to Blackbeard during their encounter.
Here comes the reach. If Shanks is tied into this, he could be a Celestial Dragon. Who else just shows up to Mary Geoise unannounced, gets an audience with the Gorosei while being “Super” (insert Franky voice) infamous, and stopping the Marineford War with almost no opposition whatever from either side…
He may have been able to tie Blackbeard to Rox through his ‘connections’ and travels on the sea and could easily be warning the Gorosei about Blackbeard being connected to Rox and doing something similar to what he did in the past. Shanks seems to have a true dislike, or at least, a very high caution level of Blackbeard. It could be that they were born to be enemies, Shanks being a Celestial Dragon and Teach being a D.
Teach WAS able to scar Shanks without the added used of Whitebeard’s fruit. That’s no easy feat.
Also, if Blackbeard was a child in secret, like Ace, that could be why it seems like he was an outcast as a child and had a poor upbringing in the picture that Oda drew of him.
Just something that I was thinking about to make one of the greatest pirates in the series, even more dangerous!
*Theory by Zach Mathis