First off Stacy, is your 2010 Insight an EX? (does it gave a usb connection in the center console?) only EX Insights have the factory alarm. If it is in fact the stock one, my suggestion would be to check the little rubber covered buttons that activate the interior lights. Those are what signal the alarm that a door is open. In other Hondas there is also a switch for the hood. Any of these things can make the alarm go off.
If you have some aftermarket alarm put on a base or LX model or some "enhancement" add on it could be a lot of other things.
By the way, one does not have to do anything beyond locking the doors to set the stock alarm. The honk on the second press adds nothing except annoyance to the neighbors. That honk is for when you are walking away in a raking lot and cannot remember if you locked the car. The "alarm is set" indicator is the flashing red light by the speedometer. The one on the radio will blink regardless.
I have not tried this in the Insight, but in my other Honda, if I use the central lock on the Passanger side to lock up, the doors are locked but no alarm is set. That might be a work around for the short term.