Perhaps your artwork has an anti-capitalist message, and you do not want it to appear anywhere near an Ad for the latest beauty cream.
In the early days of the Internet, there were places to promote a webcomic with no commerical interest, like usenet and forums, and it was typical to visit an artist's website directly.
These days, the average new Internet user might not even be aware of the concept that an artist can have their own website, and own the user experience of visitng that website from end to end. Web design in the early 2000s had a lot of creativity and easter eggs built into the experience of navigating the pages themselves.
An artist absolutely has the right to not want to upload their creative work (which takes days and weeks to produce), onto a bland social media site with it's own terms and conditions with regard how that content is treated and monetized.
Places like Instagram are bleak compared to what was pushing creative boundaries of the web in the mid to late 2000s. Sure, there are still fun websites like this but they are difficult to find (what happened to StumbleUpon?)