This question comes up almost every day, and as winter approaches, it comes up even more.
Yes, mounting two new tires on the rear of your car truly is counter-intuitive. If you never turn a corner at speeds over 5 mph your best tires could go on front. But since most of us turn, have on/off ramps and sweeping corners in our commutes, when replacing two tires they need to go on the back. It's all based on physics. Three things give your tire traction. They are not all equal. Remaining tread depth/void area typically is more than 1/3rd the equation when in adverse weather. Your tread compound and tread shape are the other two things contributing to traction.
If your tires are worn, your ability to resist hydroplaning is greatly reduced. Watch this video.
If your front tires are new and your rear tires are at 30-50% tread depth and it is raining and you are going around a sharp curve at 45 miles per hour. Your rear end starts to slide. What do you do?
1. Lift off the throttle.
2. Tap the brakes.
If you lift, the slide gets worse. If you brake, the slide gets worse. By braking or lifting you have shifted weight to the front, enlarging the contact patches on the front tires and decreasing the contact patch on the rear tires. There really isn't a good way to handle it. Steering through it while keeping the throttle constant is about the only way to have a chance at saving it.
I had the opportunity to drive a skid car at the Mid-Ohio Driving School. It is seriously tricky. The car simulates loss of traction on any specific corner of the vehicle the instructor wants, and simulates a much faster speed than you are actually going. It gave us a good picture of this scenario. Any lift or brake with the wheels turned or in a corner is ineffective.
Tire Rack always recommends that when replacing only two tires, the two newest tires should be installed on the rear axle of the vehicle. Read more.