Why count down from 8 in Lindy hop?

You mean "count down in 8 in Lindy hop".

Lindy hop is a jazz dance and is danced to music in 4/4 time. That is to say you can count 1-2-3-4 along with the music.

Historically, jazz dances (and partner dances in general) are counted in 8 for various reasons. It lines up with the music well, and you can do twice as much in eight counts as you can do in four.

Also: That's why we count ourselves in with "... five, six, seven, eight"