No bike should feel unstable. Don’t ride an unstable bike.
cyclic Eric above hits on one possible problem. And a common one. Other likely issues would be a bad headset (loose or tight, notchy or worn out) wheels not centered, wheels loose on axle, excessive tire pressure, inadequate tire pressure, saddle too high, handlebars too far away. There are probably some I missed, all on this list are very common.
No manufacturer is going to sell an unstable unsafe bike. They do not want to kill the customers. What customers will do with the bike they can’t control. Pretty much all tales of twitchy bikes are from riders who attempted to do something strange and unlikely. All race bikes in particular are quite stable. Couldn’t race them if they weren’t.