That graph really doesn't speak well to your point at all. No one ever said birth control doesn't prevent pregnancy, what I have said is there is no correlation between the proliferation of birth control and the decline in unwanted pregnancies(as they in fact have increased). Despite the declining costs and rising availability of birth control to the masses, the unwanted amount of pregnancies have increased and a large chunk of women don't use it routinely. There is no evidence making it even cheaper through government subsidy would decrease unwanted pregnancies, as it has only become cheaper and more available over the years.
I don't have a problem with the methodology, but what they have is a projection, and it doesn't mesh at all with the data that has been aggregated to date, by them no less. So I guess I will throw back your statement to you, since you have been so keen to avoid the damning data that debunks your claim of a causal relationship between the increase in birth control and decline in unwanted pregnancies(Which doesn't exist). If you have a problem with their methodology, prove them wrong that unwanted have in fact increased.
I think I will keep the discussion on teen birth rates in the thread. Because I don't agree that it is an unmitigated good like you claim. Yes, of course I oppose unwed teen births as I oppose are births out of wedlock ideally. However, I have a problem with teenagers getting married and having children, in general people defer marriage and wait too long for kids, and this has societal consequences. So to throw it back at you, I think you have issues since you callously disregard declining birth rates.
If you weren't really sure that millennials have more sex, than maybe you shouldn't be making unsubstantiated claims that young people today have more sex and this explains the rise in unwanted pregnancies, when the data shows millennials have less sexual partners than Boomers or Gen X'ers. If you have a more definite measure of sexual activity than the number of sexual partners, and can show an elevated level of sexual activity for millennials versus boomers and gen x'ers, than please, provide it.