Why doesn't this V-Brake fit my frame?

Your frame is designed for the type of cantilever brake you already had, which has pads closer to the pivot than modern brakes. Unfortunately it looks like you are stuck with your old brakes.

The old brakes can be improved with new cables and pads and lubricating the pivots.

The first thing is, do you have the right wheel size in this bike?

People often convert 27" bicycles to 700c, which requires 4 mm more adjustment downwards on the brakes (which looks about to what you need, so it wouldn't surprise me if this was the case).

In any case, you need to either:

• Try a different V-brake. Some will have more adjustment than others. Paul's Moto BMX will probably have the most possible, but is a very expensive V-brake.
• Try a compatible cantilever brake. I'd try the Tektro CR720 or similar to start (this is a standard modern cantilever brake). Some frames have problems with clearance for this, and the best option is to go to your local bike shop and source an old cantilever brake (or ebay). I've also heard that Planet X's Frog Bollox is good for this application.

Note that V-brakes and cantilever brakes use different brake levers.

Had the same problem. The answer is spacers. Each braking pad axle has two spacers one on the outer side (where you tighten the pad) and one of the inner side of the brake arm (towards the wheel). One of them is short and the other longer. You have the long spacer on the inner side (they usually come like this). It should be the other way around. Switch them and place the long on the outside and the short on the inside. Ensure that all other parts (washers eg) remain in the correct place.