My first thought is stick with white grout but i"m thinking on this....

I thought about white grout but I’m afraid it’s going to stain with the way that we cook.

I assume the small square white sample is your cabinet color and the black is for the island? What is your counter that IMO is what drives the backsplash and grout color. If I am right about these choices IMO the carpet and thr floor tile are not right. Please give us a bit more info

I assume you have children. I assume you are looking for spill and mess tolerant. I will assume the budget is strict. I will ALSO assume you will be back here asking how to bring the space to life. Don't purchase mud if you can avoid it. The selection above is better, but still heavy and dark on the carpet. Must you have wall to wall carpet in the family room is the question, and must you have tile? Sectionals are first SIZE and fit to a space. ........first things first, here.. And yes..........where IS the counter top selection., please !!?

The more I think about it, I too am leaning gray grout. Do you like this look?

[Houzz Photo white tile/gray grout[(https://www.houzz.com/photos/kitchenlab-traditional-kitchen-chicago-phvw-vp~56748)

I like a light grey grout, too.

All our white tile in our house has grey grout. I'd never choose white grout for any reason. lol

I would suggest identifying here and finalizing the selection before choosing a grout color since the items do not appear to all complement each other.

Look into oyster grey grout. It is warmer grey that looks nice with brown flooring.

My husband believes we should go with a brown grout but I can‘t picture this.

I vote for your husband's choice. I'd pick a beige that is close to the color and tone of the kitchen's floor tile. :-)

I would go with a light platinum. Just dark enough to distinguish the tiles. To me, white grout on white tiles screams bathroom not kitchen.

You don't match grout to the floor! To me, a wood floor is a neutral and stands alone.

You don't match grout to the floor! To me, a wood floor is a neutral and stands alone.

I thought the OP had tile planned for her kitchen flooring, not wood?

I had no idea I committed quite the design faux-pas by suggesting that the (pure white tiled) backsplash grout repeat the color/tone of the light-colored floor tile in the first photo, lol. Sorry!