This is a pretty broad brush statement, but most people who haven’t had a good, quality fitting at some point are probably in skates that are too big.
If you were never taught, and/or sized wrong, you buy skates a size too big to compensate for wide feet, or that boot shape didn’t fit your foot. Or too big because your are used to the proper “tight” fit of a new skate. You might buy to big because you sized them standing up straight, rather than in hockey stance. Or, the store doesn’t have your exact size and model in stock, and the underpaid and overworked person doing the fitting does their best to get you in the next closest thing.
New too big skates skates feel like a comfortable sneaker. New correct size skates feel like a sneaker that’s probably too small. When they break in, the too big skate will get even roomier, but you may not notice it, and the correct skate feels great when broken in, but you have to go through the first few skating session of adapting to a new boot with interiors that are conforming to your foot.
You see the same with snowboarding boots and skiing boots, and I assume any performance footwear. We apply the model for fitting street shoes to any footwear, because that’s all the knowledge we have. A half size isn’t off isn’t the end of the world, but you can get a bump in performance if you get that fit dialed in for your foot.