Theories I don't Support:
-Isshin is King (silly)
-Aizen and Isshin are Brothers
-Aizen "created" or is somehow related to Ichigo
Yes these would be interesting twists, but I dont suppose we have ANY reason whatsoever to really suspect these things.
My Theory:
1. Aizen's complete thought was supposed to be "because you are a Shinigami and a **Hollow**"
Truthfully, there is no reason to believe ichigo has quincy powers and the only thing we know Ichigo really is, is human, part shinigami, and part hollow. And since humans have no real consistent powers (orihime's, sado's and ishida's powers are all completely unique to them or their families) that we know of. It only makes sense that Aizen would refer to his hollow abilities in conjunction with his shinigami abilities.
2. Ichigo is the perfect mix of Hollow and Shinigami because... [this is where I go out on a limb].... Isshin was a Shinigami and his mother Masaki was a VASTO LORDE. Thus, he is the ultimate shinigami-hollow hybrid. That also explains why is conception/birth was so important to Aizen.
If you're thinking, why the hell would a shinigami and hollow fall in love/conceive a child (or multiple children), then I'd say, look at Nel. Nel is definitely a hollow, and friggin strong hollow too. But she is also pretty human-like, not only in appearance, but in dispositions, behavior, and morality and such. So it would be possible for a hollow to love a shinigami, in my opinion.
This could also help explain why ichigo kicks ass in very battle (bad-ass-ness runs in the family).
3. I'll take it one step further and say that Isshin was formerly a part of the Zero Division, which would explain why very few people (only urahara, really) knows him. Since it seems like only Captains and a few former lieutenants know about the existence of Zero Division/Royal Guard, its not a stretch of the imagination that the captains don't know very much, if anything at all, about members of that squad. And we already know that Isshin had lost his powers somehow, so it is possible that Masaki could've lost her powers as well.
Now that I think of it, Masaki HAD to be more than just a regular human. We already know that isshin is somehow special, but would it make sense (from the author's persepctive) for some former badass captain-level shinigami to marry some completely random/not-unique human, who eventually gives birth to an even more ass-kicking child? I don't think so.
Sorry about the novel. haha
PS: I think it seems obvious that Isshin is somehow related to the Shiba house. I mean, ichigo looks like kaein, isshin looks like ganju, and kukkaku looks like karin. Not to mention, they have very similar behaviors/mannerisms. I don't think its too much of a stretch to say Isshin was former head of the Shiba house.