You're new here so I don't really know how well you know the game, so if it sounds like I am patronizing you, I'm not, just being cautious and trying to cover all the bases.
What
Z
ZSaberLink
said is correct. Auto-cancelling means Link receives hard landing lag, which for us is 5 frames. The landing lag of FAir 51< is 12. To see this go to a stage in training mode and set it to 1/4 speed Hold L (Hold L allows you to stop time if you feel the need), jump once and move Link towards the opponent. Once he is above the opponent press jump again and you will jump off his head, called a footstool (this just gives you more height). At the height of your jump press jump again to get your double jump allowing you even more time. Before you reach the top of that jump press and hold down, that prevents you from falling fast. As you begin to fall slowly, press A as you are still holding down. This will make DAir come out. DAir is the easiest to tell whether it autocancels, if Link's sword strikes the ground, it did not autocancel. Hold shield and note how long before the shield pops up. There are 16 frames from the time the DAir hitboxes are present until he can act again. If Link lands in this time you will notice he lands on his feet and not with the sword in the ground, that is the autocancel. Take note at how long that lasts. Now do a full hop FAir (still in 1/4 speed Hold L) and see if the landing lag is the same as the autocancel before. You could just not do the DAir and autocancel the FAir off of a double jump to see what an actual autocancel is, but DAir is much more obvious to see. Anyhow, you should see that after the first hit of FAir the landing lag is more than twice as long, no matter when he lands.
If you are experienced enough to not need that long walkthrough, then sorry dude, you are just straight up wrong, maybe you only think it autocancels because at 1X speed 5 and 12 frames don't look too far off.