That is one sweeping statement to state everyone is selfish. While anything one does may be construed as being done with selfish motives, it is not always so. When a person starts a project or something, then he/she has the responsibility to take care of the process to its fruition. If you produce a child, you got to take care and train till the child is grown up to take care of life and hopefully make the right choices. It doesn't matter whether someone calls it being selfish or doing it with expectancy; it just needs to be taken care of.
While selfishness is inbuilt into man's thinking and actions, it is also possible to overcome that, and it has been done, is being done, and will continue to be done in future also. Of course it does take any or a combination of life events including divine intervention to bring this about, and it is not impossible. We can give names of famous people easily. And there are so many, many of those little people whom the world never hears or sees, and yet they go about their kindness and giving that will put us to shame when we actually open our eyes and see. You may find them in the vegetable market or as an auto driver or tailor or company manager or CEO or anywhere. It is better to appreciate the unselfishness of people than to sit at out devices and complain about all the selfishness that does abound. As long as God is around, you will always find something going on that is not done out of selfish motives. He is well able to change selfish natures around to the opposite direction if we allow him to.
If one wants to test this out, just go ahead and visit an orphanage or homeless people or the undertrials in prisons or refugees in war zones or any of the despised people wherever and see if you change from your own self-defined characteristic. You may never be the same again, for better or worse, but you won't be the same. You can get hardened and then carry away something that will prick the conscience; or you will be determined to do something about what you saw, and do it as is, without ulterior motives.