Why are dandelions and mushrooms classified in separate groups?

Fungi have cell walls composed of chitin instead of cellulose (usually). Fungi also lack chloroplasts and are therefore unable to perform photosynthesis. Fungi use the AAA pathway to synthesize lysine instead of the DAP pathway used by plants. Plants have multiple flagella on their motile spores while fungi only have one. The closing evidence are molecular phylogenies, which pretty consistently group fungi with animals on the tree of life.