Under what circumstances is it ethical for teachers to teach the existence of a tool such as MXtoolbox? Under what circumstances is it legal and ethical to use a superficial scan with protocol-adhering requests to scan a target that is not your own?
Portscanning a school district's web or mail server is likely to be regarded as hostile under any circumstances without working with the school's IT department. Students are likely to do so if they know about such a tool, even if warned about the consequences.
The Computer Fraud and Abuse Act (CFAA) makes it a felony to access computer resources that are not your own without written permission from the owner if such access causes $5000 damage or more. The CFAA identifies as damages the cost to investigate any potentially unauthorized use and harden the resource against such future access.
No one has ever been found guilty under the CFAA for portscanning, but only one judge has ever ruled on the matter and it is considered ambiguous under the law if it involves thousands of ports across thousands of computers, especially if the scan uses requests that do not conform to the expectations of the protocol at each corresponding port.
Ports and protocols are important concepts early in a student's learning. Tools like MXtoolbox perform non-damaging scans and send a dozen or so requests, one of which is identical to directing a web browser to the target.