It's good to transplant prior to flipping them to flower. Your plants will likely double, possibly more in height during the first 3 weeks of flowering. Giving the roots plenty of room and fresh medium is a good thing. Your partner is just wrong on this one. A healthy plant starts with healthy roots. Like DP said, 3-5 gallon containers generally work pretty well. Myself, I use either 5 or 7 gallon because I have quite a bit of vertical room to the lights, nearly 6.5' to the bottom edge of the reflectors. The larger the container you use, the larger your plants will get.

Good luck!

Farmer Rich