Here's why:

* Transverse waves have particles that oscillate perpendicular to the direction the wave travels. Imagine a rope tied to a post, if you shake it up and down, the wave travels horizontally along the rope, but the rope particles move vertically (up and down).

* Longitudinal waves have particles that oscillate parallel to the direction the wave travels. Think of a slinky. When you push a section forward, the compression travels down the slinky, but the individual coils move back and forth along the same line as the wave.

In your description, the particles moving forward at the crest and backward at the trough indicates they are moving perpendicular to the wave's direction of travel, which is the defining characteristic of a transverse wave.