The parsha covers various requirements for Israelite Priests. What it does not cover is the general concept of being a priest.
The role of priest is entered into by lineage, as the line of Aaron’s family. No choice here.
Today Israel’s priests are still identified through the various versions of the name Cohen, or Aaronson. There is actually a DNA marker which clearly identifies the priest family line. The, by the way, is a clear reason for broadening the definition of being “Jewish” since the only identifiable lineage markers run through the male chromosome. But more on that for another time.
So you can not become a priest even if you want to be one. And who wants the responsibility of being a priest anyway? Think about it!
Picture from an absolutely fascinating web site of ancient pictures
Here are some study notes: