Why has my ipad2 no software update icon showing?

That is only available after ios 5. You need to update through itunes on your computer.

Assuming your tags are correct, your are running an older version of iOS that does not include that fucntionailty (it was added beginning with 5). You will need to plug the iPAd into a computer running a current version of itunes to update. Once you have updated, you will be able wot update via WiFi moving forward.

See Updating your Device using itunes here : http://support.apple.com/kb/HT4623

If you have an iPad 1, the max iOS is 5.1.1. For newer iPads, the current iOS is 6.1.3. The Settings>General>Software Update only appears if you have iOS 5.0 or higher currently installed.

iOS 5: Updating your device to iOS 5 or Later

http://support.apple.com/kb/HT4972

How to install iOS 6

http://www.macworld.com/article/2010061/hands-on-with-ios-6-installation.html

iOS: How to update your iPhone, iPad, or iPod touch

http://support.apple.com/kb/HT4623

If you are currently running an iOS lower than 5.0, connect the iPad to the computer, open iTunes. Then select the iPad under the Devices heading on the left, click on the Summary tab and then click on Check for Update.

Tip - If connected to your computer, you may need to disable your firewall and anitvirus software temporarily. Then download and install the iOS update. Be sure and backup your iPad before the iOS update. After you update an iPad (except iPad 1) to iOS 6.x, the next update can be installed via wifi (i.e., not connected to your computer).

Tip 2 - If you're updating via wifi, place your iPad close to your router to preclude getting a corrupted download.

 Cheers, Tom 😉