I don't consider myself an expert, but I have a fairly decent understanding of radio. I belong to a club that includes a number of people who have less theoretical background.
I understand that reciprocity for an antenna means that we can calculate properties for an antenna when transmitting, when it is more intuitive and then we "hand wave" and say that reciprocity exists and because of that, we can apply the same parameters to an antenna being used in receive mode.
Is there a way to explain this to someone with less experience without having to invoke reciprocity?
Edit: the following is a secondary part of this question and is of lesser importance.
If not, is there a way to explain it to someone with more experience at a higher level than Maxwell's equations or the like?
Also I am not questioning Reciprocity, but it may not be intuitive to some. The comment by Brian K1LI may imply the best answer. "Don't try to explain without Reciprocity, but explain Reciprocity, if necessary.
Clarification by a simple example: If I want to explain why a Yagi has a null on receive, I can invoke reciprocity and say there is a null in various places or gain in various places because that is what it looks like when it is transmitting. Some people may be fine with that, especially if I explain why the principle holds, but It may not be an obvious answer.
Added April 17: I'm not sure what answer to accept. Most of them have some useful or interesting pieces, but none of them really provide a good answer to my question. What is the proper protocol on this site? I'm happy to write up an answer that is a combination of what was said by everyone, but I also want to give credit to those who have provided answers.