Is Anonymous Communication Impossible?

I'll try to keep my question short and sweet.
As the title says; Is anonymous communication impossible, or at least, for the average person, unfeasible?

Why I ask this is that I've been trying to take my online privacy more seriously recently, but everything I do seems to have a caveat that makes it only more private, not totally private.
If I use a (word this community doesn't allow that starts with v and ends with n and has a …

anonymous communication privacy