It's missing the chainstays, which are the tubes from the bottom bracket (where the pedals attach) to the rear axle.

The seatstays (the tubes from under the seat to the rear axle) are only connected to the seat tube with a small weld. When you pedal, you're using the top part of the chain to pull the rear axle toward the pedals. This force is going to break the weld connecting the seatstays to the seat tube.

Note that a chain can't push, only pull, so the bottom part of the chain cannot counterbalance this force.

The back fork should be connected to the seatpost with a pair of horizontal braces.

It's an exaggeration to say it would immediately break. But if you put weight on it, it will tend to spread out (imagine putting weight on a bent piece of metal shaped like a ^). Still, the front fork isn't braced, and bikes exist with quite a large rake angle on the front fork (think a Harley-Davidson style chopper). So maybe you can make this design strong enough to bear a person's weight.

Other people pointed out the chainstays are missing, although most people are missing out why they are important. Hint: the name tells it all!

Without them, the back "triangle" of the bike would flex, causing the distance where the chainstay would be to shorten, resulting in the chain popping off the gears, or at least causing it to skip a bunch. The chainstay causes the chain to ... stay.

Its missing the bar from the pedals to the back tire. If you sat on this bike, all your weight would rest on the joint under the seat, bending the front half of the frame away from the back tire, at least sending the pedals into the ground, if not snapping the frame outright.

It's missing the chain stays (a section of the frame linking the frame near the rear wheel to the pedal area). There would be a large cantilever arm trying to support a large part of the rider's weight, and it would likely break under the stress.

Picture the downward force generated by sitting on the bicycle causing the rear axle and bottom bracket to spread away from each other, causing the seatstays to break at the seat tube. This is what chainstays prevent on a complete frame.

It is missing the part of the frame from the rear wheel to the bottom bracket.

in addition to what others mentioned, the chain attached to both wheels will make turning.. difficult