@Mirroar Absolutely, adults usually do, and should, put their own children first - with anything that is important. Please continue reading as even though I agreed with that part of your post, I think that we probably fundamentally disagree on what we consider is putting our own children first.
All my children are adults now, and I am lucky enough to be a grandmother as well. In my opinion, the most important feelings and knowledge (age appropriate of course) for any children to have, are the feelings - and therefore knowledge - of being totally loved, totally safe, in fact for younger children, not even knowing that they feel safe, as the lack of safety and security are feelings they have no knowledge of.
Therefore, I feel that all children should be brought up by carers who only use positivity, and gentle explanations, to explain how pleased/impressed we are with anything they do, say, or produce. If it is not possible to praise them for something, maybe because it might hurt another child's feelings, or potentially it could physically harm another child or adult, or even themself, then it is imperative that we as parents/grandparents/guardians/teachers/aunts and uncles etc, explain in appropriate and gentle language, for our/their child's age, why on any particular occassion, it was not the best thing that said child could say or do.
To me, teaching my child that on certain, important, occassions, it is not always right to put himself first, but rather to take into account whether something that he wants to do for himself is likely to cause mental or physical pain to another child, due to my child breaking an earlier promise, or assurance, to that other child, to do something different, is teaching my child to not only be kind and considerate, but to keep - whenever possible - promises that he has made. I would also tell my DC that he should expect the same considerations from others as he grows up, unless the other person has some vulnerabilities that make it very hard/impossible for the other person to understand and reciprocate.
As I mentioned earlier, my children are all adults now, and although - like the rest of us - they are not perfect, they are all kind and caring people, and they are not 'doormats' or 'yes' people. So, I believe that teaching my children to not always be selfish - and doing so from a young age - is, actually, me putting them first.