In the contemporary Flash and Arrow series as well as in other superhero series, for example the DC bronze age comic books which I grew up with, the superheroes keep their secret identities from almost everybody except other superheroes (although the new TV series heroes are a little more relaxed in that regard).
They don't tell their relatives, close friends and loved ones even if it hurts or threatens to destroy those relationships. It always puts a lot of strain on them, at least. Their friends suspect something, are worried, stop trusting the heroes and so on.
The result is almost always disastrous. Barry Allen didn't tell Patty Spivot and lost her, Oliver Queen didn't tell his sister and pushed her into the arms of Malcolm Merlin, more recently Curtis Holt kept it from his loving husband and hurt him a lot when his lies became obvious. And so on.
In the bronze age, Clark Kent would always find some lame excuse when Superman was needed urgently, like telling Lois that he felt sick when some weird alien hovered over Metropolis, calling him out. Sometimes, acting out those excuses took quite some time - in those cases, the threat simply had to wait a moment, which in turn threatened other peoples lifes.
The official reason for that strategy: when asked why he didn't tell, Oliver Queen usually answers "I did it to protect her" (Stephen Amell pronounces tect with a lot of breath while widening his mouth and showing his teeth for emphasis). Superman/Clark had the same idea: protect your friends.
Obviously, not telling your spouse your secret identity helps you if s/he gets tortured and then can't tell the enemy who you really are.
But how can keeping that other identity from the person you love and trust possibly help that person? Any example?