Why does pulling out main speakers from wall improve sound?

That question interests me as well.  I have always assumed that it would add depth to the sound stage. 

To round out room reflections. An alternative is wall absorption treatment. Or live with image confusion.

Obviously "your" dealer is more interested in sales than good sound.

Sound radiates out and around each speaker until it bounces off the nearest hard vertical surface. If you have treated walls, it can be mitigated in the upper octaves. Too close to the front wall, and side walls can cause too much lower octaves.

The room is small, about 13.5x13.9x8.

In my treated room, the speakers are less than a foot from the front wall, and 3 feet from one side, 4 feet from the other side wall.

Because of the treatment, I get a true 3D soundstage if the recording is done well.

About half of my collection is recorded well, or very well.

PS, my speakers are deep, about 18". So the drivers are all about 30" from the front wall.

Simple answer: Because they are designed to work that way. Mostly due to the increased use of subwoofers the speakers no longer need the bass reinforcement of a near wall or near corner set-up.