Is it permitted to induce labor?
Many doctors prefer to induce labor rather than let it happen naturally for the very important medical reason that they play golf on Sundays with a fellow doctor and don't want to bothered while involved in "chashuva inyanim" on the links.
The problem is that it is forbidden according to halacha unless there is a true medical reason [i.e. the health of the mother or fetus] to do so. Many reasons have been offered as to why it is forbidden. One is that a person's time of birth affects who he or she is and speeding it up is going against Hashem's plan.
Another is that giving birth is dangerous and one is not allowed to actively being upon this danger. When it comes - it comes [and we have an assurance that the woman in most cases will be fine]...
See the Medical Halachic Encyclopedia of Dr. Avraham Steinberg for many sources Page 273.
As an aside, since we are on the topic... Despite its widespread practice, taking birth control is against Jewish law. In order to take it, one needs a heter from a competent Rav. If he gives blanket heterim to everybody then he is not competent... We want to increase the number of Jewish children in the world. That is our first mitzva of the 613 and also our answer to Hitler, Hamas etc. etc. ym"sh. וד"ל.
לזכות נעכא גיטל בת רחל אסתר לזרעא חייא וקיימא זרעא די לא יפסוק ודי לא יבטול מפתגמי אורייתא