You are not specifying what IDA version you are using and if at all you are trying to run the code that could be debugged by IDA on the machine that you are running it, but there might be another case.
Chris Eagle in this The IDA Pro Book writes...
IDA attempts to warn you of this possibility anytime you select Debugger → Start Process (or Debugger →
Attach to process with an open database) by displaying a debugger warning
message stating the following:
You are going to launch the debugger. Debugging a program
means that its code will be executed on your system.
Be careful with malicious programs, viruses and trojans!
REMARK: if you select ‘No’, the debugger will be automatically
Are you sure you want to continue?
Selecting No in response to this warning causes the Debugger menu
to be removed from the IDA menu bar. The Debugger menu will not be
restored until you close the active database.
So maybe at one point you've answered
no and IDA remembers this in the database? Try new analysis from scratch to see if the menu gets restored.