Because they look identical (obviously, stylized art, but still). Of course, there are dizygotic twins (i.e. not identical) but it still seems to me like it's easier to just claim they're not twins at all. And seriously - you don't find their insistence that they're not twins the least bit fishy?
I'm not saying they are twins, just that the possibility is there until Jeph confirms it outside of the comic (which he already might have, for all I know).
Its also a possibility that Marten is really a martian, I mean, Hey, Jeph hasn't stated that he isn't!, but I consider it highly unlikely. (and this requires even less stretching because Marten has never claimed he isn't either (that I remember))
The whole twin thing just sounds like two siblings who look very similar who are tired of being called twins.
Lying about their ages is just a weird thing to do. Let's say for arguments sake that you are right.
Either
A) She is lying about her own age and is really 21, and if so, amazing job getting to grad school that young. And most people who manage something like that are very PROUD of doing that, and are not likely to want to lie and say they are older.
or
B) She is lying about her brothers age, and I'm sorry, I wouldn't agree to claiming I'm 3 years younger than I am just to cover someones paranoia.
or
C) She is lying about BOTH Of their ages, and I think we all agree this is the most absurd option.
Either way, this continued charade would require one of them to not be able to celebrate their birthdays at the appropriate time, and all on the OFF chance that someone would go "hey these two twins look the same, but are opposite genders, ever think they might have BOTH been assigned as male at birth". Some siblings look remarkably alike, some twins of opposite gender look very similar. They do come from the same genetic stock after all.
The idea that they are actually twins and are lying about it is such a stretch of any form of logic. Its just patently absurd to consider.
(Also, go back through their interactions. Claire reads VERY MUCH like the elder sibling in their interactions.)