I just updated to iOS 10 and I want to send an SMS instead of an iMessage to a friend. In iOS 9 I could continuously touch an old message and press
send as a text message (or something like that). Now in iOS 10 I don't see anything relevant.
So, does the other person have an iPhone or something else? If it's something else, then it will automatically send as an sms. If the messages fails to send, and you try multiple times to send it, it will ask if you want to send as an sms instead of an iMessage (at least I think it will still do that).
If anything else, you could always go into iMessage settings, sign out of your Apple ID and then turn off and on iMessage.
This is still available but you first need to enable 'Send as SMS' under the global settings for the messages app. (I assume this is off by default, as I had the same trouble as the questioner.)
Once you have enabled the option, then there is an extra menu entry when you hold down on the message (the reactions menu will pop up, and an action sheet at the bottom with 'Copy', 'Send as Text Message', and 'More...' will appear).
If you haven't turned on 'Send as SMS' in messages settings the menu will only contain 'Copy' and 'More...' - this also seems to be true for any messages you sent before enabling the option. So you need to send a new iMessage first, then press and hold on that while it is sending or after it has been sent.
Not sure about iOS 10 but I figured out a way that works in iOS 11 and posted this video example: https://www.youtube.com/watch?v=ih3ABR9lswE
What you need to do is tap on the message right after you send it and then a menu pops up that lets you choose "Send as Text Message".
This doesn't always work for some reason but I think has to do if your current thread is sending to a phone number versus an email address that's tied to an Apple ID.