As mentioned, stats show that only 2-3% of term policies pay out. In most cases they are cancelled or expire before a claim is ever made.
If you are looking to make sure you have something to leave the kids 20-30 years from now, Whole Life insurance is the only way to go. Based on the information you provided this is what you need. That being said, it is important to meet with an liscensed insurance broker to fully assess your needs to make sure that you are not buying too much whole life if you don't need it, when term insurance can cover some of your needs. Only deal with a broker who has access to multiple companies and both term and whole life. One trick ponies will only give you the reasons to buy thier policy and not give you well rounded advice that suits your situation. They will just try to squeeze a square peg into a round hole...
Term has a specific purpose. A temporary need, like covering debts that will go away eventually, making sure young children will get taken care of until they can care for themselves, etc. The catch is you have to die within a specified time period to get anythign out of the policy.
Whole Life also has a specific purpose. It's for long term needs, such as leaving a legacy fund or money for your family, covering final expenses, etc, no matter when you die.
The Buy Term and Invest the Rest theory is severely flawed. It's not horrible, you just need to be careful with it and make sure you have a very well rounded plan with safety nets incase something bad happens. Just ask any 60 year old today that started with this strategey 30 years ago. Right now, their insurance premiums on their term insurance would be a horrendously high premium if they still have it, and all the rest that they invested is worth as little as 30% of what it was planned for and they are going into retirement withdrawing their money for a loss with no safety net if something severe happens to their family. For those that used this strategey and thought they were self insured enough and cancelled thier insurance, will be leaving no where near the amount of money they thought they would. The returns on this strategey are completely shot. When it's a Bull Market this strategey looks like gold, just like any other investment strategy, but when the bear markets and recessions hit, you find out whether your strategey is really good or just a flash in the pan when everything is doing well.