I want to turn off two-factor authentication its annoying me.

See Two-factor authentication for Apple ID https://support.apple.com/en-us/HT204915 and more specifically the section entitled Can I turn off two-factor authentication after I’ve turned it on? This section says: 

"If you recently updated your account, you can unenroll within two weeks of enrollment. Just open your enrollment confirmation email and click the link to return to your previous security settings. Keep in mind, this makes your account less secure and means that you can't use features that require higher security."

This quote emphasizes the security-related importance of two-factor authentication. I would not turn it off even if you are able to. Another reason for not turning it off is that if you use two-factor authentication, then you no longer will have a need for security questions. They are turned off when two-factor authentication is activated.

anna.dahlia wrote:

Not sure if you’ve tried this lately, but when I most recently tried this that very frustrating evening, I could no longer access Find My without a code. I couldn’t access any portion of ICloud without that code.

It's still an option for me:

Here is why I’m very frustrated with not being able to turn this off:

1) it does not only prompt me for this 2-factor authentication when signing in to new devices. It prompts me over and over even though I select “trust this device.” example: just right now, while logging into this site..... I had to verify it was me while only using my phone. My phone doesn’t even remember to trust ITS OWN BROWSER.

2) I left my phone at a friends house the other night. When I got home, I was already very tired and ready for bed. And then I couldn’t find my phone. I tried logging into find my iPhone—but nope—wouldn’t allow me to play that lost sound or see where it was without having the codes which were all sent to my lost phone. SO FRUSTRATING. I had to dig out an old retired iPad, wait for it charge enough to turn on (it’s an old edition) to finally locate my phone. I have my phone on silent 90% of the time because I work in an office, so I usually can’t call it/hear it without playing that lost sound.

Another contentious event in this diatribe—I emailed Apple beseeching they turn this off 3 or 4 weeks ago. Apple has still not sent so much as form email reply back to me. Not a peep.

It is beyond me why Apple would create this option and then cement their customers in and not simply give us the option to turn it off if we so choose.

jeanne1884 wrote:

It is ridiculous and very annoying. Also why doesnt my wifi doesnt lock to my router. Apple is robbing us!

Exactly what has Apple stolen from you? They've decreased, significantly, the likelihood that your iCloud account will be compromised.

As for the WiFi issue, that's a completely separate issue. I suggest you start your own thread with a subject line that describes your problem. You're much more likely to get help that way.

anna.dahlia wrote:

2) I left my phone at a friends house the other night. When I got home, I was already very tired and ready for bed. And then I couldn’t find my phone. I tried logging into find my iPhone—but nope—wouldn’t allow me to play that lost sound or see where it was without having the codes which were all sent to my lost phone.

You can log into iCloud and access Find My Phone without needing the code. There's an option for it at the bottom of the iCloud log in page.

However, it's wise to have another phone set up as a trusted device. I have my work landline set up as one. It can be a friend or family member's phone. It can be a landline or Android.

I actually did try logging into iCloud and yes— you’re right— you didn’t need a code at one point in time to select “find my iPhone.”

Not sure if you’ve tried this lately, but when I most recently tried this that very frustrating evening, I could no longer access Find My without a code. I couldn’t access any portion of ICloud without that code.

You only have 2 weeks to turn it off....

https://setapp.com/how-to/turn-off-two-factor-authentication-for-apple-id

How exactly, is it 'annoying' you?

It should be completely unobtrusive. You should only be prompted to authenticate with 2 factor when signing into your iCloud account on a new device.

It is ridiculous and very annoying. Also why doesnt my wifi doesnt lock to my router. Apple is robbing us!