I decided my female protag went into the army and was assigned to be a combat engineer (so good building skills), where she met her husband. When she finished her tour of duty, she got her law degree with a G.I. Bill scholarship. Her specialty was legal advocacy for veterans. She is high Str and Cha, good at building and talking to people mainly, but familiar enough with weapons she knows which end to point at the enemy. She's finding herself a good fit for leading the Minutemen, not only for a military background but also a legal one, where she hopes she can establish eventually a proper rule of law for her settlements.
Likewise, since male protag is supposed to be "giving a speech" at the beginning of the game, once can presume he has more skills/education than just what he learned in the army. He might also have a degree, like in poli sci or something. Or not!
On one hand, it's weird they added such specific background to the main protagonists, on the other, people can be multi-skilled and multi-task and have rich histories. I'm thinking about another female protagonist playthrough where she got her vanity-degree from a correspondence course and is no more qualified to be in a court than a teddy bear. Another who was a criminal in her youth, who survived horrible things in juvie, and studied law to find ways to better protect and rehabilitate underaged inmates. And so on.
Likewise with the male protag---what other education he might have, or not, what his upbringing was like, what unit he served in all can result in very different characters. Was he a chaplain, a sniper, infantry, MP, or medic? Etc.