You are onto something. Yes, it don't make sense to relate a thing to itself. Its like tautology. Not wrong but not useful either.
Ofcourse a thing is similar to itself, even more, its same to itself. What do you get from it? That things don't change on their own. A one year old is well aware of that.
Now, its useful to compare a thing to itself in past or in future. People say "you have grown up" or "you are getting weak". They are comparing you from today to you from past. Two different things so the comparison is useful.
In mathematics when its said "x for all x such that..." they are not comparing a thing to itself. They are comparing a thing to an idea of the thing, an object to the die its casted from.
Its like having a table. The columns define how data in it should be. For example we decide to put a person's name, father name and date of birth in a table; 3 columns. Now each row is the object, it should fit in the table. The table is the die. Object is whats casted. We cannot for example store 4 data points about a person in the table, it has to be 3 data points. Data casted become a row in the table.
Its like having variables. The mathematics line says that pick anything, lets call it x, as long as its fitted in the die i.e. have such and such properties like this another x thats already casted, it has such and such other properties as well or the function give such and such output.