Why can't I sign in to my ipod touch 2g using my apple id ?

Most lilkely you have 2 factor authentication on on your Apple ID. It could be that the iPod touch is running a too old iOS version in order to support logging in with 2 factor authentication. To login with 2 factor authentication you must have iOS 9 on the iPod

If the iPod is running an earlier iOS version, you will first need to generate a verification code at another place, at an iPhone for example

If your device is online:

1. Go to Settings > [your name].
2. Tap Password & Security > Get Verification Code.

If your device is offline:

1. Go to Settings > [your name].
2. Tap Password & Security. 
3. A message states “Account Details Unavailable”. Tap Get Verification Code.

You can also generate a verification code from your Mac if you have one

1. ]Go to Apple menu  > System Preferences, then click Apple ID.
2. Click Password & Security > Get Verification Code.

When you continue to sign in at your iPad, put this verification code in the field where you would normally put your Apple ID password. If everything goes well, you can sign in now