You’re leaning heavily on transitivity. In areas, such as maths where identity can be defined precisely transitivity holds: If a=b and b=c, then a=c. But it doesn’t have to where identity is fuzzy. If I define identity99 as “a is 99% similar to b”, then “a is identical99 to b” and “b is identical99 to c” don’t imply “a is identical99 to c”.
You’re leaning heavily on transitivity. In areas, such as maths where identity can be defined precisely transitivity holds: If a=b and b=c, then a=c. But it doesn’t have to where identity is fuzzy. If I define identity99 as “a is 99% similar to b”, then “a is identical99 to b” and “b is identical99 to c” don’t imply “a is identical99 to c”.