Can Men Become Nuns?

Dr. King, you are stumbling over a definitional problem in attempting to draw your analogy.  All you need to do is take down the dictionary from your shelf and look up nun" and "priest."
 
As long as "nun" is defined as someone who (1) does or believes A, B, C, D, . . .  and (2) is female, then no, men cannot become nuns by definition.  Drop (2) from the definition, and then yes, they can.  It is a matter of definition.  Humans define this word, not God.  And humans can change the definition (although in my opinion it is pointless to do so).
 
The definition of "priest," however, does not carry a gender-specific element, as there are female priests in other denominations.
 
Humans define words.  And also roles.  Certain roles for women in society and elsewhere, by convention rather than by divine ordination, are a part of our culture.  But culture can change.