All equalities by definition require two different things. In 1+1=2, we presume that 1=1.
However, although the two different 1's in 1=1 can either refer to a single object or two objects which we consider similar, we demand they have to refer to two different objects in 1+1. We don't count the same object twice.
Although we agree to ignore/ not consider the differences between the two entities in 1+1 to treat them as similar, we don't really stay true to our own conditions. We make use of those differences to be able to tell the two things apart. It's like saying 'the differences don't matter at all — the two things are similar', while also saying 'come on, we all know that they are different things' . We are simultaneously aware and not aware of the differences.
The concept of '2' require similar-different objects, and such can only exist in our subjective perception.
I would love to know your opinion regard this.
Read my argument in detail here: Math is Subjective