Background for anyone who may not know: I, an EU citizen, have the right to enter any EU or Schengen state (in this case Italy) using either a passport or national ID card. It doesn't matter whether I fly from the UK, Turkey or even the US; Italy is Italy and so EU law applies.

The issue at hand: just flew Chisinau-Kyiv-Milan, and, at passport control in Milan, presented my ID card, but once the officer found I had flown from Kyiv, rejected it and demanded a passport, which I didn't have. He also demanded my boarding passes, which I had left on the respective aircraft.

I politely but firmly explained to him that, per the EU freedom of movement directive, I have the right to enter, and that it shouldn't matter to him where I flew from, but I might as well have been talking to the wall.

I was taken into custody for potential deportees where I was held for over an hour, partly involving two officers asking totally irrelevant questions such as whether I had a ticket back home (which I didn't as it was a re-routed flight - I took trains ticketless back home) and insisted that, having flown from a non-EU state, I couldn't enter Italy on my ID card.

Eventually, though, I was handed back my ID and let go with no further explanation.

I've already got an email address to send a complaint to.

What I'd like to know is if, besides demanding a proper lecture of the officer at the booth (whose ID number I noted down, which he clearly disliked) and a written apology from the chief officer, I could also demand financial compensation for being (in the end) 2 hours delayed back home because of this event, seeing as I was held for a completely illegitimate reason.

Answer

Can I get financial compensation?

Can you first quantify in euros how much damage you suffered from detention? If yes, consult a lawyer asking if there is any rule granting you compensation. If no, you can't demand anything.

Quantification can be done by means of missed connection and suffered costs.

Airline compensation fees for missed connections or denied boarding are a different thing. They are a legal provision to protect customers under a common event, to avoid them to document, prove and sue an airline for suffered damage. Anything else must be discussed in court and handled individually. Your case is unique enough.

I've already got an email address to send a complaint to.

Yes, you can politely address the issue to the manager. I hope they gave you a real, official and monitored address.

Raising flags and suspicion

Border officers look for exceptions to the norm, because that is where the cases they are paid to find usually dwell (cit. @JimMacKenzie)

The problem here is that the immigration officers were simply doing their jobs and were alerted by important alert flags that you have raised with them during primary inspection.

1. 
   You were trying to enter the Schengen area without a passport. This is not usually a concern, but some kind of soft flag. There are a number of countries that accept national IDs rather than passports. An officer looking at your ID has the right to ask where you are coming from. And you have the right to explain why you can travel without owning a passport. For example, you could be coming from UK which is still EU. Milan (Malpensa?) is a very large airport with plenties of destinations. A lot of people fly without passport without concerns.


2. 
   You (claimed you) were coming from Ukraine. Ukraine has no agreement with Italy for recognition of ID cards (unlike Moldova-Sweden). This is a serious yellow flag at this point. The officer knows that in order to arrive from Ukraine you have needed a passport there. Need to investigate!


3. 
   You (claimed to) have left the boarding cards on board. Along with the two above, you triggered an alarm in the officer's mind. Now, it is true that you have no obligation to keep your cards until exit from the airport. But you just collected 3 alert flags in a single shot!!

Since you had 3 elements of suspicion, questioning was a bare minimum. You did not mention yours and the officers' behaviour in the conversation. You politely but firmly demanded to be allowed to enter Italy according to Schengen rules. Okay, let's assume politely... but when a person firmly claims a right on legal standings, I would immediately summon my manager or my legal office!

It is my assumption, from the interpretation of the question, that you were just standing on your legal point without trying to explain the particular situation. Particularly because you were allowed a connection in KBP without a transit visa. I think (again, it's my thought) you just repeatedly answered them "Why the heck do you need a passport when I am European?", instead of cooperating with the police explaining how your situation was special on your favour.

During your detention, they might have done additional checks without telling you, like criminal records, arrest warrants and effective records of exit from Schengen area, just to make sure there was no reason to drag additional attention on you. They could have even phoned the Swedish embassy to clarify, or their legal team. Who knows. In the end, you were rightfully released as expected.

There was no reason to hold you indefintely, but it took them some time to determine you are welcome.

An example

Following is mere speculation.

To help you understand why it was important in such a situation (not just a Swede entering Italy without a passport, but the above 3 flags all together), let me try to enter the officers' shoes and provide examples.

You are a passenger standing next to me with a Swedish ID card after a flight from Ukraine.

Could you have bribed someone to let you board the aircraft's illegally (even along the baggage?) and then emerge at destination? That might explain your lack of boarding cards. Investigate!

Could you have given your passport to someone looking like you to continue traveling on your name? Investigate!

Is it possible that your passport has been recently confiscated, but not your ID, under a criminal prosecution in order not to leave the country? Call embassy, investigate!

Yet again, that is speculation.

Conclusion

In the end, I hope that you will have a polite written conversation with the officers' management. You will unlikely get real apologies for what happened, but maybe they will explain to you why your situation demanded additional attention at the airport.

I'd say the chance to get any kind of financial compensation is low. There is no compensation provision in Schengen Borders Code, and I doubt there is one in the Italian national law.

You can pursue the court case against them, but note that even Article 8 gives the border officials leeway:

However, on a non-systematic basis, when carrying out minimum checks
on persons enjoying the right of free movement under Union law, border
guards may consult national and European databases in order to ensure
that such persons do not represent a genuine, present and sufficiently
serious threat to the internal security, public policy, international
relations of the Member States or a threat to the public health.

Note that there is no limitation on how long this "consulting" should take, and - unlike the rest of #2 in Article 8 - it is not required to be "minimal" or "rapid".

And of course they can claim they had suspicion about the validity of your documents - and until the validity is established, they cannot admit you as EU citizen. Here a point could be made that the border guard lacked proper training. But again its unlikely there is a law which would compensate you for having to deal with untrained government servant.

I think you are out of luck because in my understanding, the officer was right and you were wrong. Well, the officer is always right to begin with, but in this case, he really is.

You correctly state that as an EU citizen you have the right to move freely within the territory of the Member States and need nothing but an ID card. Ukraine is not a member state, so... you did not simply enter a member state's territory, but you did enter the Union's territory from God-knows-where (Ukraine in that case, and Moldavia before that, which also is non-EU) with merely an ID card. Which not only makes you "unusual" compared to most everyone else, but the ID card is also an item that is almost routinely refurbished for illegitimate purposes because of its sucks-so-much security features.

While it is indisputable that as a proven EU citizen you are finally entitled to enter and stay without limit^[1] -- what else, you have nowhere else to go -- it is perfectly legitimate to hold you back and do some plausibility checks when there's reasonable doubt. Because, well, you need to prove without doubt that you are indeed a citizen to have the rights that you claim.

I think it's highly unlikely (read as: impossible) that you will be able to prove that there was no reasonable doubt, so trying to get at the officer is pretty much a waste of your time.

I don't think you have any chance here.

Generalizing your problem:

The basic premise, opposite of what happens now would be that, if you were delayed in a security queue by the officer you would get a compensation for that.

The practical result of such rule would be that the border police would be pressured to avoid any delays to cut down any costs. And, in last resort the officer himself could be considered responsible for the delay, if he didn't have any good explanation. Suspecting someone would not be enough, because that would be applied in all delay situations and you would have a similar system.
No government or organization will want that kind of pressure, because the result, can be a very poor security check. No one wants that responsibility in their hands.