I'll make a list:
1) Better sleep for everyone. In a standard room, DS will stay awake past his bedtime because Mommy and Daddy are RIGHT THERE and they're not asleep yet, so he thinks he can stay up, too! If we have a condo, we can close the door and he will be able to calm down and unwind enough to take a good nap or sleep through the night. Rarely happens when we share a room.
2) We love to unwind in our room during naps or after DS's bedtime. We can have the TV and lights on, we can talk, we can take a nice hot bath in the whirlpool tub with some Epsom salts and rest our legs for another day in the parks.
3) The kitchen. It's so nice to be able to eat breakfast in the room or to get our coffee fix. I bring our Keurig Mini and for the price we'd pay for 2 small coffees at a Disney resort, I can get a box of K Cups and some travel cups from Dollar Tree. Next trip, I will be stopping at Publix to buy eggs, bacon, Uncrustables (DS fell in love with these on the last trip, but they are a major ripoff in the parks), and some more stuff to eat. I can spend money on so-so CS food or save by cooking a few meals and putting that money toward better meals in the parks.
4) Convenience. We have never been more than 20-25 minutes from the park gates to our hotel (maybe MK is an exception). It's easy to head back to your offsite resort for a midday break as long as you're not too far from WDW.
5) Value. If we didn't stay offsite, we couldn't go. Plain and simple. We are staying at WBC in a few weeks and we are paying less than $100/night for a 2 bedroom condo. That is unheard of on property. If we insisted on staying on site, we'd have to save for a few years. There is no way we could've afforded to buy APs or to visit more than once this year if we'd done that.
6) Some people get Disney'd out. My DH did not grow up drinking the Disney Kool-Aid and needs a break from all the fun.

That may not apply to your family, but it makes him happy to go to a "normal" hotel and have a "normal" meal at the end of the day.