A Necessary Choice…
Two-Step verification is a security measure which requires your Apple ID password and a verification code when your Apple ID is used to sign in to your account (either via Settings or via a browser). These two pieces of information together protect any information (documents, photos, etc.) which you have saved to your iCloud account, including Photo Library.
Without the verification code (which is sent to “Trusted Phone Number” when you select “Allow”) sign-in is thwarted. This is great if someone gains access to your password – select “Don’t Allow” and immediately change your Apple ID password.
While the security process is highly recommended, you MUST keep the list of “Trusted Phone Numbers” up to date (and have at least one in addition to your own which you could gain access to should you not have access the primary number.) Additional numbers may prevent you from being locked out of your own account should your own device be inaccessible!
If you were – say – to lose your phone, you could find its location by signing in to your account via the Find My iPhone App on a friend’s phone. However in the absence of the App, you could not access to your account via a iCloud.com without a verification code, which is most likely set to be sent to the lost phone. Given this situation, you can chose “Didn’t get a verification code?” from the browser and have the code sent to another trusted phone number.