For me, there is one single reason spaces are superior to tabs, and that reason is the most important: it ensures that you, the reader, are viewing my code exactly as I, the author, wrote it.

Consider this snippet, where tabs (⇥) equal four spaces (·) in my editor:

    if (someCondition) {
    ⇥   Foo foo = SomeClass::SomeFunctionCall(myParameter1,
    ⇥   ⇥   ⇥   ⇥   ⇥   ⇥   ⇥   ⇥   ⇥   ··myParameter2,
    ⇥   ⇥   ⇥   ⇥   ⇥   ⇥   ⇥   ⇥   ⇥   ··myParameterN);
    }

Looks good.

Now you open this snippet in your IDE, where tabs are set to two spaces:

    if (someCondition) {
    ⇥ Foo foo = SomeClass::SomeFunctionCall(myParameter1,
    ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ ··myParameter2,
    ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ ··myParameterN);
    }

This matters more when the presentation is important, like I might write ASCII diagrams in my code, are have a large matrix with elements aligned, or similar.