Are compact and subcompact cars safe?

I ask because my mom says that, for example, a Honda Fit or even a Civic aren't safe cars. She says the smallest Honda I could drive is an Accord (and I know they don't have a sedan larger than that). So, is it true that cars like the Civic and Fit aren't safe?

No this is old school thinking where the thought runs, bigger is safer. NHTSA proves otherwise. The Fit actually outperformed the Accord in safety by quite a bit in passenger side collisions. Spend some time at the link below for some myth busting information. Mom doesn't know everything but that's OK because her heart is in the right place. Yes No - they are in fact built to very good standards of occupant protection.
If even an Accord is hit by a truck it will not end well
Old folks think small cars are less safe - not always the case now They're safe enough, until you get T-BONED by a Hummer going 70 MPH, then, you're dead meat brother. His bumper is going to crash through your side window at about the level of your chin. OUCH.

Actually, the odds are way in your favor… Do you feel lucky, PUNK?

No - they are in fact built to very good standards of occupant protection.
If even an Accord is hit by a truck it will not end well
Old folks think small cars are less safe - not always the case now

They're safe enough, until you get T-BONED by a Hummer going 70 MPH, then, you're dead meat brother. His bumper is going to crash through your side window at about the level of your chin. OUCH.

Actually, the odds are way in your favor… Do you feel lucky, PUNK?