So here's an odd question. My wife and I had planned to pay for a booking between the US and Denmark this summer, with our 6 month old travelling as a lap infant. We were prepared to pay 10% of the fare as his lap infant price, BUT the Delta agent just told my wife that even children between 0-2 need to buy full tickets, whether they use a separate seat or not. I couldn't believe this so I looked on the delta website, and it states in relevant part that an "infant in arms" on an international flight costs 10%, but that "YOU WILL NEED TO PURCHASE A TICKET FOR YOUR CHILD IF YOU: Will be traveling between countries, regardless of whether or not the child occupies a seat."

What type of international travel doesn't involve travelling between countries? Is there some sort of terminology either the agent or I am misunderstanding here?

https://www.delta.com/us/en/children.../infant-travel