Same as I'd feel if DH wanted the 8 year old to do swimming/choir/dancing/knitting/any other activity.
If the 8 year old was also keen and we could afford it and it fitted round other commitments then they could go ahead and start. Otherwise they wouldn't.
Kick boxing for an 8 year old is going to be mostly about flexibility and fitness. If OP has reservations I would suggest that she goes to watch a class to find out what it involves.
I found it very interesting that quite a few posters have assumed that OP has a DS despite her not stating this (and several other posters talking about their DDs doing kick boxing). Just shows how many preconceptions people have.