Where do they get the idea that birth control is a bad thing? Do they have any scripture they use to try to support this view?
The true reason is that the Roman Catholic Church needs many many Roman Catholic babies in order to survive and stay in power, simple as that. That's the reason they support Viagra, because in a Catholic marriage Viagra = more Catholic babies.
At the beginning of Christianity, 2,000 years or so ago, staying single and not having babies was encouraged. Jesus did not marry or have children. Paul did not marry or have children, and he encouraged other Christians to do the same if they had the ability to abstain from sexual immorality. Getting married and having "Godly offspring"(Malachi 2:15) was of course not discouraged either. Either was fine.
The growth of Christianity in the first century was due to spreading the Gospel and making new converts, not on having lots of Christian babies. All that changed a few centuries later, mainly thanks to the Roman Catholic Church.