What does a vicious streak a mile wide mean?

Answer 1

As a literary device, the idea of a streak of color on the back of a person is analogous to the white stripe on the back of a skunk. A skunk is what it is; it cannot decide to change. The wider the stripe, the worse the attribute.

So a "yellow streak" refers to cowardice. A "mean streak" or a "vicious streak" describes the person as having that attribute. Because the attribute is inherent, you cannot choose NOT to be mean or vicious; at best, these can be suppressed but never eliminated.