What Israel is doing now is not “defending” Israel (that horse left the barn on October 7th when it took 20 hours for Israel to even get any soldiers to the area outside Gaza where so many were so heinously murdered or abducted).
Nor is it going after Hamas–in fact, it is recruiting lots of new members for Hamas.
It is wreaking vengeance on innocent Gazans to pay Hamas back for targeting innocent Israelis (why else tell Gazans to go to southern Gaza and then bomb the refugees in southern Gaza over and over?) and saving face for the IDF who failed to defend Israel in the first place.