Eye tests are inherently flawed. Not only have eyes/memory been proven to be unreliable and subject to bias, and not only do casual fans generally have no idea what to look for, but even if they did, they don't have the ability to watch all 6 of their team's players on the ice at the same time, let alone all 12 individuals on the ice at the same time, let alone all 12 individuals on the ice in all games at the same time. Everybody watches different players doing different things at different times and understands what they see in different ways to draw different conclusions. The end result is an entirely qualitative measure that is 100% based on personal feelings, and there is no way to verify the reliability, truthfulness, or consistency of the methods they use. There is no information learned other than how that one individual feels, which makes it useless for the purposes of discussion. It also makes it useless for the purposes of determining contract value.
There is no inherent bias in stats. They can't be wrong. They are just numbers that show what happened on the ice. The only place bias can enter is in how they are used or interpreted, but they can be checked by outside sources, challenged, discussed, and improved. The methods are out there for everybody to see, the numbers are verified, and it promotes discussion. Context can be accounted for properly, and more context has been added repeatedly by Zeke, myself, and others posting stats to try and get a clearer picture.
The problem here is not people disagreeing with how to best utilize the stats and what context to add to get the clearest picture. The problem here is people outright dismissing the stats and relying on their own feelings over any useful quantitative measure because it doesn't match with their preconceived ideas.