Let’s just get one thing straight about authorship. It is a political statement. Like all political statements, it is highly subject to dispute, but also has some underlying truth. Authorship is a convention and the conventions are different in different fields. Authorship rules also change with time. If you want my overall philosophy, it is to fit in with your field and to be generous both with authorship and issues like author order and who is senior or corresponding author.
When I was trying to decide what laboratory to join as an undergraduate, I first visited a neurobiology lab on the med campus at Michigan (almost no one knows this, but it is true). The kindly professor showed me around a bit and gave me a few reprints. I also met his technician. I don’t remember how it came up, but I will never forget what the professor told me about authorship. It was that the technician did a great deal of the work and got her credit in the acknowledgements, which was just what she wanted, he explained. Right then and there I decided that being acknowledged was not what I wanted and did not join that lab.
Chandra Jack, first author and corresponding author, https://peerj.com/articles/1352/
But 40 years ago it is probably true that technicians were more likely to be acknowledged than to be in the author list. That has changed. Many other things have changed, like the size of collaborating groups and what constitutes a publishable unit. I could write about who gets to be first author, senior author, or last author. But instead for now I’ll focus on something else, corresponding author.
The corresponding author is the one who gets a little indication by their name for correspondence and then their contact information is given, at least an email address. I opened the latest issue of Evolution and see that for one paper Erik Svensson is both first author and is the one with an email address, though no formal designation of corresponding author is given. The next paper I opened from the same issue of Evolution has the last author, Nick Royle, as the one with an email. How about PLoS Biology? Planarians has a little envelope sign by the last author, as does a CNS myelination paper. It seems like the corresponding author is being used here to indicate whose lab the work was done in. How about ecology? Also in PLoS Biology, from January, a paper on forest biodiversity has the little envelope by the first two authors. Another paper has it by both the first and last author. In the journal, Ecology, it was the first author with the little envelope on all of the papers I checked.
What does corresponding author really mean when we can usually easily find the email of any author we choose? Are they really the only one we should communicate with? Does the corresponding author tell the official party line about the study, leaving out all the difficulties?
I think corresponding author is being used to claim leadership for the work. This is probably really annoying for postdocs and graduate students who would like to be the one to talk about their own work. But the PIs of the lab might feel ownership also, even if they didn’t do the hands-on work, particularly if the project was part of a grant they wrote. If you are looking for a rule on how to balance these two legitimate kinds of claims, probably between first and last authors, it is a good idea to think about who will automatically get credit and who might benefit from more recognition. Under this criterion, corresponding author should go to the earlier-career person.
Oh, of course corresponding author has nothing to do at all with who paid for anything, publications or otherwise. And, no, it is not just about who handles the paperwork of the submission. It is a political statement. From among the qualified authors, use it to benefit the newest person where it can do the most good.
Sociobiology 
The corresponding author handles official correspondence from the journal concerning the paper. It is not an honorific, it is a responsibility.
For example, the corresponding author must be in a position to get approval from other authors about the content, copyright forms, and any author fees or page charges. The corresponding author will receive the reviews, and those reviews often refer to particular parts of the paper or particular experiments, so the corresponding author must be a person who can prompt the authors responsible for a particular section to respond to the details of the review, perform changes or additional experiments if necessary. Once the paper is published, other people may write critical letters or comments to the editor of the journal, and the journal will be forward these to the corresponding author, for possible reply.
The first author of a paper may be in a good position to carry out official correspondence, but not always, particularly in large collaborations where the different authors do not know each other well.
Yes, it seems like it is just the technical detail of who handles the correspondence during submission of the paper, not political at all. But that is not what it has become. It is the person in charge of the paper. If that is always the lab head of a big group, in fact, that person will pass off the actual work to the scientist that did the most of the study, usually the first author. I maintain it is an honorific indicator of whose work it really is, or at least that is how it is used. Otherwise, why would people argue about it? Why would It be a thing at all? I can also say that junior authors are more aware and sensitive to this issue than are senior authors or lab heads. If it is just a job, not an honorific at all, and the first author wants it, why exactly is the PI unwilling to agree? He or she could specify to the junior person that it would be a good idea, or even required to pass everything by them before sending it on.
Shouldn’t the corresponding author be the person who corresponded about the paper? That seems definitionally correct.
You might be surprised how many first authors want to be corresponding authors and don’t get to be. I can see from your publications that you freely let first authors handle the correspondence.
Corresponding author should be the one (or the ones) who can best address questions that a reader my have about a publication (e.g., questions about details of analyses that are not clear from the Methods; availability of raw data or scripts used), or who knows best who of the co-authors can address such questions and round up pertinent information. Corresponding author is therefore often either the first author (who presumably contributed the most critical work) or the senior author (who presumably was instrumental in generating the research questions, guiding the research, and is ultimately responsible for research integrity, data-management, curation of data, etc).
One option is shared corresponding authorship, typically the first and the last author. Most journals allow that.
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