How would you connect a dipole (balanced system) to an unbalanced receiver? Problem is the dipole is not grounded and the receiver terminal is.
The balun not only overcomes the grounding half the signal problem it also add common mode rejection. As that antenna lead travels down from the attic it is subject to various noises. Terminal 1 and 2 feed the signal out of phase and the transformer passes it to the secondary. Noise arrives in phase and the center tap of the transformer disposes of them without any going to the secondary.