Do you understand why such a statement would be incorrect? The “anni” part of “anniversary” refers to a period covering one year. That’s how we get terms like biannual and semiannual, as well as annuity and per annum. It makes sense to say that you are celebrating a ten-year anniversary, because you’re discussing a period of ten years.
It does not make sense, then, to discuss a six-month anniversary, because it does not refer to a number of years. There’s nothing inherently wrong with celebrating the first six months of a new relationship. That’s great. Go out and have a nice dinner… just don’t call it an anniversary. You could say that you are celebrating your first six months together. You might say that you’ve reached a milestone. The exact wording is up to you.
On a somewhat related tangent, I recently missed the five-year anniversary of Beyond the Rhetoric. This blog launched way back on March 30, 2006. At the time, I was using GoDaddy’s built-in blogging software (which was terrible). Many things have changed on this blog since then and I anticipate many more changes to come in the future. I hope you stick around to join me. 🙂