I don't see how giving samples of formula discourages BF. That's absurd. If people want to BF, they will and they will try however hard works for them. If they decide it's not for them, so be it. I highly doubt anyone chose not to BF because their hospital gave free samples.
I want to address this because it is important for those who really want to try to BF to know and understand. I in no way am saying that I am anti-formula however.
The reality is that breastfeeding is really not easy mentally or physically, but it can be incredibly rewarding. During that first few weeks you will worry that your baby is not getting enough food because you can't measure exactly what they are getting. You will most likely worry that they are not getting enough food when they cry and you can't calm them down. It is really hard, and having a back up of formula is one of those things that you will break out when you are exhausted and confused and overwhelmed. I would strongly suggest you NOT have any in the house. But when the samples have been sent home with you by the hospital staff, it feels wasteful to throw it away, and every new mother who intends to BF worries that she won't be able to, so you hold onto them.
I know that the first time my husband watched our DD alone so I could run to the store I told him to not give her a bottle of formula. I had just fed her, and she WAS NOT hungry. Well, he panicked and gave her bottle when he had changed, cuddled, and run out of guesses. When I got home I popped a boob in her mouth and she calmed down instantly while the milk just ran out of her mouth and all over my lap. She wasn't hungry, she wanted mommy, but the formula made him feel he was doing something.
Bfing takes a few weeks before the feeling of reward starts to overtake you. For those first weeks it is exhausting and overwhelming, and you are still recovering so you are already down. It is very tempting to let daddy take that 2:00am feeding one week into sleep deprivation, and that is very often the start of the end.