That doesn't make it the average. Sorry, but mean and median have distinctly different meanings. For a distribution that is truly symmetrical, the median may equal the mean, but that does imply the concepts are the same. In that case, the value of the mean equals the value of median.It's the most common meaning, not the only meaning. Stat data all too often uses the median without mentioning it.
Of course the concepts are different. They're both described as "average", though.