There is no "negative" in alternating current. What you have in a 240v. supply is two 120v circuits that are 180 degrees out of phase with each other. When one is going positive, the other leg is going negative. The neutral only functions if there is an unbalanced load, more hooked to one leg than the other. Then the neutral completes the circuit for the excess amperage. If you have a balanced 240v load, like a well pump that runs on 240v. or a 240v. water heater, you do not need a neutral, just two hot legs and a ground. If you hook a light bulb to the generator, then you need a neutral. Everybody hooks up light bulbs, toasters, microwaves, etc., so a neutral is required.
If you pull the cover off of your house service panel, you will see two hot leads serving two breaker buss lines, and loads on either side in a rough attempt to balance the load. The neutral will be connected to a bunch of screw lugs along the side, and the neutral buss will also be bonded to the building ground. In theory, that keeps stray voltages from showing up on the neutral leg in 120v. circuits. In practice, the building ground can have up to a 25 ohm resistance, so there can be pretty good voltage on the neutral. That is why your generator instruction sheet will tell you to ground the generator. If you rely on the neutral, your generator frame can have enough voltage to give you a nasty shock if your feet are wet.
That NEMA 14-50 plug has provisions for two hots, a neutral, and a ground. How it wires to the transfer switch depends on the design of the transfer switch. It may feed a 2-pole breaker or it may wire to main lugs. The neutral and ground will both be bonded at the box. That is why a local ground for the generator frame is a really good idea. The neutral can pick up stray voltages just like the main electrical panel.