In my opinion this is a major curse on the internet today and it's usually large corporations who "don't understand" that do it, but in this case it's a supposedly modern internet-based company, gocompare.com.
The problem is requiring more information from the user than you actually need to perform an action. In this case it's unsubscribing from a mailing list, but I've seen plenty of examples around the web that do this in other situations.
To unsubscribe my email address from a mailing list you need nothing more than my email address. FACT! Requiring me to remember the password I used to sign up 12 months ago to a service I never thought I'd need to log into again is just plain annoying. And as for requiring my date of birth, why?
"For security" I hear you cry. For what? Why would anyone want to maliciously unsubscribe me from getting reminded that my car insurance is due? It's just not gonna happen.
As I've stated in a previous blog entry, if someone wants to unsubscribe from your mailing list there is absolutely no commercial benefit to making it difficult to accomplish. I don't want your emails so forcing me to continue getting them is going to do nothing but annoy me which will likely put me off using your company for anything ever again.