You, I, my nephew and everybody else are:

((African) great) apes
(old world) monkeys
(dry nosed) primates
((placental) live-bearing) mammals
amniotes
tetrapods
((lobe-finned) bony) fish (paraphyletically)
(jawed) vertebrates
chordates
((anal*) bilateral) animals
eukaryotes

*some licence here for a suitable adjective to differentiate between those like us and echinoderms whose blastopore becomes our anus and those like arthropods and molluscs where it becomes their mouth. Now you can stop wondering about dog greetings, and about calling whales fish.