Thats not very nice of the doctor! Babies engage when they are ready - many first babies do engage early, but on the other hand, many also engage when you are in labour or just before it starts. I know of many babies born perfectly fine when they hadn't engaged until labour, even at homebirths - no dramas.

A doctor cannot tell you how wide / big your pelvis is without looking at you. It's bollocks. A pelvis scan is just as bad - your pelvis is effected by hormones and opens wide in labour. I wouldn't fall for his scare tactics - unless there is clearly something wrong with the baby (which obviously there is not, only baby isnt ready to engage yet) you don't have to agree to anything - you can just say NO! There is no law about it. CPD or cephalo-pelvic disproportion is VERY rare. Where its usually seen is where there has been prior damage to the pelvis or rickets.