Due to get induced next Thursday March 1st at 38 weeks

so yesterday at my 37 week check-up I had an ultrasound done because they saw that I was measuring about 32 to 33 weeks and on the ultrasound they said that baby was measuring about 4 lb, they said everything looked good his heartbeat, Lungs, the placenta all of that and then when the doctor checked me he said that baby felt about 5 lb and they also told me there ultrasounds can be off by a pound as well, he also told me I was dilated to 3cm and could go before next Thursday. My doctor told me they don't want me to go full term which confuses me why they would want to induce me early then if he's small.. one of my girlfriends told me the same happen to her and that she was induced due to baby being small because they felt he would due better outside of the womb. Anyone else heard of this or have this happen to them? I'm a bit concerned.