Openly sharing your genetic information makes both you AND your relatives more vulnerable, with vulnerability decreasing as relatedness decreases. It also reveals potentially sensitive information about family traits.
Can you follow the argument if we flip it around? Your right to do anything you want should include not making it public. Others publishing "theirs" would mean publishing yours, whether you want it or not.
Over 99.9% of the genome is identical to every human being. And that genome is made public (the reference genome) and updated regularly as we understand more about the DNA.
Even identical twins don't have the same DNA. So it's not like I make public another person's DNA.
It's not, I can publish/sell/do whatever I want with any of my genomic data I have desire to