The rules for cousins are actually pretty interesting and can be extended to be more comprehensive.
A 1st cousin is a descendant of your parent's siblings, a 2nd cousin is a descendant of your parent's parent's siblings, a 3rd cousin is a descendant of your parent's parent's parent's siblings and so on. Actual siblings can quite reasonably be called "0th cousins" and this fits the pattern in a logical and mathematically satisfying way.
Also, there's a concept of "double cousins" where one pair of siblings marries another pair of siblings - they're double-cousins by the fact that they can trace cousin-hood from either their mother's side or father's side. If you extend the concept that siblings are 0th-cousins, then a full sibling is in fact a double-0th-cousin while a half-sibling is a single-0th-cousin. However ... since everyone traces back to common ancestors, everyone is really double-cousins by definition, but your cousin-level (as in 1st cousin, 2nd cousin, 3rd cousin and so forth) is different on your mother's side vs father's side. We just call them double-cousins when the cousin-level on both sides of the tree is the same.
How it works that you can be your own cousin is that if you go back far enough on your mother's side and father's side you share common ancestors, therefore by the rules you can work out what cousin-type you'd be to yourself if your were separate people. So you could be your own 17th-cousin by the rules as outlined, since there are multiple lines of inheritance that connect you with the same common ancestor.