There are a couple known reasons that Visio 2016 will report "Cannot start IzoT CT". One reason is that the Visio Option "Enable Automation events" may be unchecked.
If you don't see the IzoT CT "Add-Ins" menu in Visio then this may
also be caused by "Enabled Automation events" being unchecked or the
Add-ons path not being seen.
Close CT or Visio 2016. Open
Visio 2016 directly (not through IzoT CT). Click the “File” Menu (you
may need to create a Blank Drawing first before you see the Visio
Menus), click “Options” and then “Advanced”.
1. Check if "Enable Automation events" is unchecked.
If the "Enable Automation events" checkbox is unchecked then check and click OK. Exit Visio and try running CT again. If "Enable Automation events" checkbox checked go to step 2.
2. Replace Add-ons path.
Even though the path may be correct, removing the path text and then re-adding it fixes most issues.
If you still see an issue. Exit CT and Visio and start Visio directly. Go back to "File > Options > Advanced". Scroll down and click the "File Locations..." button. Copy the entire text from the "Add-ons" field and save it to a notepad file.
Delete all the text from Add-ons field, click OK and close Visio.
Start Visio directly, Go back to the File Locations and paste back
the previous text, press OK and exit Visio. Try running CT again.
If you still have issues please see the following KB articles:
1. KB1346 - See #5, Supported Visio 2016 version and required service pack
2. KB1349 - Visio 2016 Trust Center Settings