Within the framework of the story, it's reasonable to assume that Aela and Skjor are giving you the choice at that point because, bless his heart, that big lunkhead Farkas transformed in front of a newbie and spilled the beans about the Circle's little secret. From their point of view, I think it's more about getting another werewolf into the fold than it is about allowing you into the Circle because of who you are and what you've done. IMO they're just looking for another ally in their vendetta against the Silver Hand and they think forcing you to become like them will secure your cooperation and loyalty and bind you to their cause in a way that wouldn't be possible otherwise.
(When I first played to that point, I really thought I was being offered a choice between becoming like them or being killed. I saw it as a much more "do this or else" moment, and it was kinda surprised to find out that I could refuse and all it did was stall the questline.)
It makes sense given the attitudes of everyone involved. There are five members of the Circle (counting Kodlak). The oldest and wisest, their Harbinger, is trying to cure himself and it's hinted at if not outright assumed that the twins will follow in his footsteps if he succeeds. Aela and Skjor don't want a cure, they see lycanthropy as a blessing, they are eager to remain werewolves forever and to continue the tradition within the faction. But they are outnumbered. The fact that Farkas lets the cat (dog?) out of the bag gives them an excuse to pull you in on what they assume will be their side, after all *they* are the ones who are giving you this great honor. The other members of the Circle are conspicuous by their absence in the Underforge and I doubt they were ever consulted about it. I find it hard to believe that Kodlak would've said, "oh sure fine, turn the rookie into a werewolf, no problem."
In short, they have their own agenda and hope to use you to further it, and it's doubtful that they gave the rest of the Circle any opportunity to object or override their decision. Aela as much as admits that they are hiding things from the others when she says she's "running interference" for you while you're off killing Silver Hand on her orders, and doesn't think anybody else has figured out what you're up to. It was never about you being worthy of joining the CIrcle, it was about needing someone to go do her (and Skjor's) dirty work without arousing too much suspicion.
It's one of the reasons why I dislike her so much. And Skjor, but then he's not around that long. I find it hilarious that it all ends up with Kodlak naming me the next Harbinger, and that I can finish out the questline by curing myself and the twins without ever finding those precious Totems of Hircine for her. Who's outnumbered now, beeyotch?

That said - I do think it should be possible to delay the onset of the werewolf stuff more than what's possible right now. At least let me get a few more radiant quests from the rest of the Circle before everybody starts telling me to talk to Skjor. From a story perspective, I think it's justifiable the way it is - from a gameplaying perspective, it doesn't let you sink into the faction and enjoy it very much before things really start rolling.