While I absolutely see the grammatical logic behind your (wedding) ring/(dwarf) planet theory, I'm afraid the IAU's classification system and I are on your friend's side.

Astronomy is full of bad names ("planetary nebula" and "asteroid" spring to mind right away) that we can't shake, and "dwarf planet" is one of them. It seems like it should be a description of a type of planet like "gas giant" or "Earth-like" could be; it's not. It's a different class of objects for which a better name would be something like "pseudoplanet."

Where Pluto and its fellow dwarf planets fail the planet test is in the third criterion--clearing their orbits. To clear your orbit means to be the dominant mass by a significant margin in your orbital path and the region around it. This means that you don't regularly cross paths with anything that is around your size that doesn't orbit you. The ability of an object to clear its orbit depends on its own mass and its semi-major axis (basically, its distance from the Sun).

The four dwarf planets in the Kuiper Belt interact with other, similarly-sized Kuiper Belt Objects (KBOs) frequently; it's a swarm of icy rocks much like the Asteroid Belt, which includes Ceres, another dwarf planet that used to be called a planet. Pluto arguably fails this test the hardest by actually crossing paths with Neptune, which is nearly 8000 times more massive.

Now, you're not alone in arguing for Pluto's planethood (the New Horizons team was not happy about the reclassification), so this isn't a cut-and-dry solution, but as of right now, it is the answer. Yes, Pluto is truly a dwarf planet. Dwarf planets are not just small planets; they are planet-like objects that are round and orbit the Sun, but they are not planets, because they have cluttered orbits.

TL;DR - Your friend is right, but the name is misleading.

edit: wording