Everyone will give you there opinion. I'm barely 3 days over due and I haven't stopped hearing about inducing or trying this and this to help me go into labor since. It does annoy me so much but if your doctor didn't say anything about inducing you until now then you're fine. He's the professional if he would of seen anything wrong with baby or with you he would of talked to you about inducing earlier. Just enjoy your last days of being pregnant and when someone says something be like baby will be here soon.
I'm in your exact position. Was due the 25th, going in tomorrow for an ultrasound and non stress test and then will see what my options are. They also want to discuss induction with me, but we'll see what the results are. If you and the baby are fine that's all they should be cognizant of. Yes, there are things that happen when the baby is at risk, but that's why you've been checked. Some of my family also worries about the fact that I'm over the due date but I've explained to them the same thing as you, it's only and eta. They could be wrong by one week before or after and you can healthily deliver a baby at 42 weeks if all is good. Try to relax before your induction on the third and stop explaining things to others who ae frustrating you. I would prefer the baby come on its own, but if they need to induce I will do what is best for the baby. Who knows our little ones might arrive on their own! Good luck and enjoy your birth experience :-)