People have several reasons not to.
For example, the Catholic church doesn't believe in hormonal/barrier methods. People would say it is because they want to produce as many Catholics as possible.
Some people don't do it on a teleological argument, which is pretty much where the Catholic church stands, although I feel they inaccurately use the Onan story to support their argument.
In fact, most people don't realize that all churches saw BC as sinful until 1930. In 1930 the Anglican church was the first to say it is OK in marriage but only for serious reasons (whatever that means).
Most churches made BC acceptable in 1963 (is it any coincidence that it was a few years after the pill became widely used and available?)
The Catholic church refused to acquiesce, with the pope citing BC as leading to the encouragement of sexual immorality, which is true on some level, as once the fear of disease (condoms) and pregnancy (the pill) went out the window, the sexual revolution went into full swing. Which isn't to say that BC makes people immoral. All it does is to take away some of the consequences of immorality that would otherwise keep only some people behaving.
I also had a Catholic person argue to me that he sees sex as a reflection of the trinity. The man and woman are the representation of Christ and his relationship with the church. The man and woman have sex and produce a child (3 persons).
Some people even feel that withholding bodily fluids (condoms) is not really giving yourself to someone.
Also, there is the fear of causing failed implantation due to luteal phase defect that hormones cause. However since BC works primarily by supressing ovulation, the chance of this happening is very small, and almost impossible to study because how do you know if a woman conceived before she implants? We test pregnancy via hCG. EPF apparently can but is too expensive and difficult to be viable. So, for people who feel strongly convicted about life beginning at conception, they many not even want to take a micro-chance of causing the failure of a pregnancy.
I don't necessarily believe these arguments. I see and respect the stance, and at the same time, a part of me just doesn't feel birth control (hormonal and barrier) is right. Perhaps it is the teleology of it, and the side effects of the hormones. I don't know.
But, you won't catch me with 10 kids...So, my stance, until I can be convinced otherwise, is if you are married or for medical reasons, it is okay. Also, for societal reasons, if you are going to screw around, please spare us the disease and unwanted/unplanned pregnancies.
. I am very excited and at times ready to be blessed with children. I always am careful to try and remain unselfish in my desires to think that children will be the end all to my "youth" 
. If there is anymore input it is greatly appreciated, just a topic that I have never felt people (I know) were willing to discuss in the past.
