Advisor wants first author. Do I have any leverage?

Although Buffy's advice to let this go is practical, and I agree that would be perfectly fine, I think you have a second option here. Namely, if you are careful, you can bring up your concern with the advisor. However, if you do this, you shouldn't phrase it as an accusation or a claim that someone else should be first author; that would be unnecessarily antagonistic and probably would not help your case.

Instead, you could phrase it as a question. Say that you would like to understand how authorship order is determined better. Although you assume that the author order has already been agreed upon for this particular paper, as a starting researcher you are curious about the etiquette of authorship. You can ask if it is common for the PI to be first author in your area. Depending on how receptive he is, you can ask other questions.

If you follow this approach, then probably one of two things will happen:

• First, he could become defensive and dismissive. This is more likely if he is really being unethical. In this case, Buffy is probably right that your best bet is to let this go for now. Sadly, these things happen; author order isn't always determined correctly, and that can be either due to honest error or due to dishonesty. You could always talk to another professor or mentor for moral support and to assess how to proceed (particularly for future projects), but probably for this one accepting the order is not such a big deal in the grand scheme of things.

• Second, he could be helpful and receptive. Maybe he will explain that he is usually first author on his papers. Perhaps he has a good reason for this. For example, in some fields, that is accepted, while in others that is pretty condemned (I don't know what is the case for your field). But he could also have some personal justification for why to go against the convention. I would not agree with him, but perhaps if he explains this then it would make it easier for you to understand.

Whatever you decide, try to see the bigger picture that authorship is not always obvious, and this professor will be judged for his own actions by colleagues and the community in the future; it's to some extent out of your hands. Good luck.

The idea was his. He guided you throughout, giving ideas ("try this"). He seems to clearly have been the "team leader" from what you say. In the absence of any dramatically different information or analysis, I suggest that you let this go. You get a publication. It isn't a doctoral thesis. You gained knowledge that will help you later. Lots of good things here.

And, in general, fighting with advisors is a poor career move.

But, in future projects, especially when the idea for the research comes from you, settle the question of first authorship at the start. Or, just decline to participate, citing other commitments.

In fact, even in this case, it was settled at (or near) the start. And if there were many participants, it may not be clear that anyone else has a better claim.

Depending you your field, this is a typical thing. Even when the PI is listed last on a paper, many (not all) people assume that it was the PI that "really" did the work.

I agree with @Buffy that you should let this go and not bring it up. Even in a veiled-yet-transparent way, as @6005 suggested (I don't see any way you could bring that up, now, in a way that doesn't create needless conflict with the person helping you through your early career).

I'm fortunate to be in a field (econ) where the order of authorship is always alphabetical, so this doesn't come up. But even here, there's a fairly famous story of a firmly-established, well-known professor telling one of his grad students something like: "This is great work, and will for sure get published. It was sufficiently your own that you can publish it with yourself as the only author. If you do so, it will go to a good journal. Now, if you want to put my name on it also, then it will surely be published by the best journal in the field. The choice is entirely yours."

The story goes that the student opted to put his advisers name on, and sure enough, was published in the top journal.

My point here is that, rightly or wrongly, you shouldn't think of authorship as strictly merit based. Right now, despite everything you wrote, it strikes me as utterly normal that the professor overseeing undergraduate researchers would be the first author. Instead of fretting over it, be very happy that you're getting authorship as an undergrad (maybe that's normal in your field; in my that's incredibly rare), and then think toward the future.

Regardless, congrats on having a professor who is this interested in doing research with someone who is still early in their undergraduate career! It certainly speaks well to your work so far.