Clara was 26 (though Yvette Mimieux was 20) and the father thought Fabrizio was 20 (he was 23 actually, was was the actor George Hamilton). So that's a 3 year difference which is really nothing. I guess that was just a plot device.
For who would bear the whips and scorns of Hollywood... (;-p)
The father was objecting, horrified, really, when he thought Fabrizio was 20. A sic year difference is quite a bit. One is a kid, maybe in college, the other is out of school, an adult. (Worse if the older one is the woman, first it seems more 'fitting' for the man to be older, and second, a woman is less fertile as she ages.) As soon as the father found out it was only a 3 year difference, he brightened right up and dropped his objections.
Another issue was her 'purity'. It was no question to him that a 20 yro was innocent, but as she got into her later twenties there was more a chance this wasn't her first love.