This is a great question, and I too was concerned about the IAHP's approach to early learning, but on the other side of the push issue. As an new preschool teacher, I loved what I learned at the Better Baby Institute. It made me a better preschool "teacher" while giving up much of what I thought about early learning and had been learning about teaching. After many years of observation, my conclusion: Pushing, as a long term strategy, doesn't work. It will backfire and cause resentment, but more importantly, it can cause our child to resist our support when we become seen as "the pusher." But we parents don't know what does work. That is, we don't know what to replace pushing with that works, and neither did I. I was doing it in my classroom, but didn't know how to pass it on to other teachers and parents. I do now. My suggestion is always 1) see what your child's reaction is when you decide to push and don't back down, 2) notice if you are under any stress when you feel the need to push, and 3) what messages are you giving your child when you are pushing? Do you not trust the learning process? Do you want your child to do what he or she should do, from your point of view and upbringing? Are you concerned he or she isn't smart enough, or needs to be on some learning track, like we were in school? See what you see, and make your choice. There is no right or wrong way. What we do as parents either enhances our child's natural love of learning or inhibits it, and you can tell which if you look to see.
Pushing our child is motivated on one level by our love and concern, no question - and wanting our child to be successful. On the other hand, pushing is about what we want or think we need, not what is necessarily best for our child at the moment.