Illegal questioning?

First and foremost, if any passenger is refused entry on arrival at their destination the carrier is responsible for returning the passenger to their point of origin at the carrier's expense. This is not exclusive to airlines nor to the US and, in the case of the UK, the carrier is subject to substantial fines.
It follows that the carrier will wish to be sure that all passengers will be allowed entry on arrival.
Whether you are obliged to answer any questions is a moot point but the carrier is not obliged to accept you as a passenger so a flat refusal on your part might not be your best plan. On the other hand, a polite enquiry as to why you are being questioned is perfectly reasonable.

When you say, girl working for the airline---was it the person asking you questions prior to check in (person who also asks who packed your luggage, etc), or the person at the actual check in desk who gives you the boarding pass?

Sometimes I travel often to the USA and I was surprised one time when i saw one of the ladies who asks these type of questions working the Delta airline queue, when I had seen her just a month before in the American Airlines queue.

I mentioned this to her and she said she didn't work for the airline, but for the airport security or something like that, and they rotated airlines.

Also, the type of questioning asked to you is usual for those who travel with a visa. If you don't have a visa and you're part of the visa waiver program, maybe you fitted some profile because I travel with colleagues to the usa and they don't get asked to show proof of their work.

As far as answering the questions, you can do so politely and curtly. For giggles I guess you can tell them, proof of work? Is that a new policy? Because nowhere did it say to bring proof of work to board the plane to the usa. But be aware that yea, if you choose not to answer, you can be either sent for additional screening or be denied to board the plane, you know, for security reasons. ;)

And did you fly an american carrier? We have noticed that non american carriers don't even ask security questions, so next time maybe stay away from the usual american carriers and maybe you'll have a better experience.

Can there be such a thing as an illegal question?

they can ask you anything they want. If you question who they are, ask for ID. If they work for the airline, the airport, security, etc., you have two choices: answer truthfully and fly or don't answer and be left behind. Very simple. Agree that flying is quite intrusive but thats the way it is these days. Totally sucks. Stay home or drive.

You are not obliged to answer their questions, but similarly, they are not obliged to allow you on the plane.

Hi B unfortunately the. U.S. do have some strange rules, we had to clear customs to sit for two hours in a secured departure longue, this involved removing shoes etc. this was midpoint in a long haul flight! We had already cleared security in Belgium to gain access to the first leg. I've had my all my baggage carry on and hold bound being xrayed prior to being able to put it in the hold. This was not long after the Locabie plane crash caused by a suitcase bomb.
I am sad to say that this woman has a responsibility to ensure that people who are going on a flight intend to return, why did you find it. Embarrassing to tell her your job? If she asked for proof then maybe you had it maybe you didn't, but either way she is entitled to be sure your are a bonifidi traveller not someone whose aim is to become illegal in the US. It's like when they swab your be hike forexplosivesitz all due to the state of the workday afraid, soil you are a valid travelleritisannoying but that's all.

Ophs to say silly autocorrect