That is a bit of a misconception. Your front brake is much more effective at stopping the bike than the rear. People go over the handlebars because they are not gripping well enough. They are not used to the force. With a bit of practice you will never go over the handlebars with the front brake.

The rear brake is much more likely to cause a fall. When you apply the brake the bike tips forward and the rear wheel rises up. It easily looses grip and can lock up. That causes a skid and next thing you are on the ground. Or just smashed into whatever you are trying to avoid.

The front brake does not do this because the tipping forward pushes the front wheel into the ground. You get more grip and more braking potential. With a little practice you can stop the bike quickly and easily. You will never go back. But you have to grip the handlebars and tense your arms a bit to deal with the force.