All of what we've seen Homura do so far makes perfect sense if we interpret her actions and words through the prism of her being Madoka from the future.
Suppose that in the original timeline Madoka chose to be a magical girl in order to save Sayaka. She may have also had the recently deceased Mami in the back of her mind, so she wished for what one could vaguely call "displacement" powers. This could account for Homura's flight, teleportation, and ability to make bombs and laser beams appear out of nowhere. A bow as a weapon also seems fitting to me for a person with displacement powers. Since Homura has displacement powers, she can also change her place in the time stream.
Homura (i.e. future Madoka) wished for these powers, in part, on the hope to go back into the past to save Mami, after she saved Sayaka.
However, after future Madoka chose to be a magical girl, something very bad happened quickly thereafter, and as a result of that choice. This makes future Madoka regret ever becoming a magical girl.
Perhaps larger time jumps require building up (or cleansing) a lot of energy through many witch eliminations. So future Madoka (Homura) needed a lot of time to get all the needed energy to go far enough back in time.
Over that time, she became very hardened through seeing many fellow magical girls die, and the old Madoka died with them, psychologically speaking. In other words, her earlier idealism and optimism died, and future Madoka became the cynical Homura.
But now Homura has traveled back into the past, hoping to prevent what happened.
She targets past Kyubey since with him gone, her past self can never become a magical girl. Homura may also greatly resent Kyubey for how he smooth-talked her into becoming a magical girl. Finally, Mami getting involved caused Homura to back off, since Homura (future Madoka) just couldn't bring herself to hurt the same Mami that she liked a lot when she first met Mami in the original timeline.
Homura then tries to take Mami's place in that fight from Episode 3. She does this because she wants to prevent Mami's death (as it occurred in the original timeline from the exact same fight). But because Homura has been so hardened by what she has seen in life, seeing Mami's death again doesn't affect her as much as it did the first time she saw it.
Homura reacts negatively to Sayaka choosing to be a magical girl, because that puts things one key step closer to Madoka choosing to be a magical girl. She tells her younger self to give up on Sayaka since she knows that if Madoka
doesn't do this, she might very well make the same choice that Homura did in the original timeline. Also, Homura will take it upon herself to defend Sayaka anyway, as Sayaka was her dear friend in the original timeline.
Some of Homura's words to Madoka are harsh because she resents her younger self for being so naively idealistic, as she now sees it.
However, she also knows (from her memories) how sincere and noble her younger self's feelings are, so she can't help but to have some affection for her younger self, and wish that she could still be that way herself.
Some other supporting hints for this speculation here:
1) Kyubey doesn't seem to know much about Homura. This is because she's from the future.
2) Homura is clearly very powerful, even for a magical girl. This would reflect well what Kyubey said about Madoka's high degree of potential.
3) Madoka's dream in the first episode could be tied into all of this. Perhaps a residual affect of Homura time traveling is that it sent a vision to her past self via a dream. That vision is of the future of the original timeline, where Homura confronts a massive monster that was created, in part, from Homura choosing to be a magical girl.
4) Why does the OP have two Madokas (and one a slightly taller one, I think)? Now, OPs can have all sorts of trippy stuff in them (SHAFT's especially
), but the way it's played up so heavily is highly suggestive to me. Well, if Homura is future Madoka, then those scenes in the OP of two Madokas starts to make a lot of sense...
5) Madoka and Homura both have bows as their primary weapon, at least in official promotional artwork. Maybe a sly way for the writer to make a connection between Homura/Madoka and
Archer/Shirou of Fate/Stay Night.
Anyway, that's all for now. What do people think of this speculation here?