How to combine Buddhism with being a parent? Buddhist philosophy says that we shouldn't get attached and try to form bonds with something and desire or crave it because everything is essentially impermanent and this will lead to suffering. But how can you raise a child without being attached? Wouldn't that make you lousy parent? 

Of course the older a child gets, the more you'll have to let go. Every child needs to find his/her own way in life, but that doesn't take away the fact that, especially in the early years, there is a big attachment to your children. 

Perhaps I am misunderstanding the concept of attachment? Or is there another explanation?
Parents are supposed to practice Brahmavihara towards children. Attachment doesn't benefit them in any way. What benefits them are kindness, compassion, empathetic joy and equanimity. Attachment or clinging just makes you sad and afraid. Lord Buddha had no attachment. But he still preached the Dhamma, Vinaya and created a system which benefited many beings. Sometimes he would travel a great distance to help people attain enlightenment. He advised the Arya Sangha to do the same. Even after 2500 years, millions of people around the world still benefit from it. All that good work is done because of compassion. Not because of attachment.

You provide for your children because of Metta (friendliness). 
When they get sick, you take them to the doctor because of Karuna (compassion).
When they study well and get into good positions in the society, you become happy because of Muditha (sympathetic joy).
When they get married and leave you or when they get busy in life and don't visit you as much as they used to, you stay calm because of Upekkha (equanimity).

Attachment doesn't do any of that. It only makes you sad &amp; afraid.