Kalev son of Yefunne
Kalev was called a Kenizzite because he was the STEPSON
of Kenaz. After Kalev's father Yefunne died, his widowed mother married
Kenaz and bore him Otni'el. Since Kalev was raised in the household of Kenaz he
was called "the Kenizzite." This should be obvious since Torah specifically
instructs in Num. 2:2 that one's Tribal heritage
is through the ancestory of their father, Kalev became the leader of the Tribe
of Yehudah, therefore his father had to have been an
Israelite.