Honestly, this isn't about who is right or wrong, but whether you are okay tolerating this behavior towards your children? I have two young children and I would not be okay with someone treating them this way. My H and I have slightly different philosophies and I am certainly more nurturing and ready to give praise and he would say I coddle and spoil a bit. But he is loving and is good about praising, he just feels they should be pushed to do things on their own sooner than I force them to.
Do you live together? Really think about what his behavior is doing to your kids.