I'm afraid you are arguing with the simplified non-scientific definitions. Did you think I was making the complexity up? The reality of our classification system is a mess, like most classification systems, since nature doesn't care what labels we attach.

• The scientific definition of an asteroid is actually a combination of several factors, including where the asteroid resides (inside Jupiter's orbit? A Trojan? A Greek?), it's size, it's composition (just basically not entirely icy), and it's historical origin. This gets exceptionally complex when you take into account and icy body in the asteroid belt (we know of many), a comet that has burned off it's ice, an ejected asteroid in strange orbits, an asteroid orbiting a planet (see Mars' moons), a body that otherwise meets criteria as an asteroid that is larger than the other asteroids (Ceres etc).... Generally scientists today don't use 'asteroid' in technical writing, they prefer 'minor planet'.
• The scientific definition of meteor/meteoroid/meteorite means that any body can become a meteor if it's in the right conditions, but it'll still be a meteoroid/comet/asteroid/moon/dwarf planet too. It's nearly useless as a set of definitions, especially when the meanings of the same words have changed consistently since the founding of modern astronomy.
• A comets definition, like that of an asteroid, is actually tied to its location (oort cloud? Kuiper belt? elliptical orbit? Stable orbit past Jupiter? Currently orbiting a planet? Currently close enough to the sun?), speed (influences if it can form a coma), temperature (influences if it can form a coma), composition (influences if it can form a coma), historical origin (oort cloud? Kuiper belt?). It's another definition rarely used by scientists outside scientific communication because it lacks a firm foundation to stand on.