What is wrong with this radiator support...

OK, it took me a minute to figure out what you're saying, but yeah, if it has a 65 radiator support, the side panels would have to be moved in to make the radiator opening 63 sized. Your driver's side looks like the right piece to me (just eyeballing). What does your passenger side piece look like? Because the 63 panel on that side does look different than later ones.

Edit: Here's a 65 Barracuda radiator support I found on ebay:
View attachment 1715472403

This looks like a larger (A/C maybe) radiator for the '65.