Frank does not have any day-to-day responsibilities with his daughter or grandson, or with a hostile parent. No pressures there. If he did feel sorry for Erin and bought her diapers and baby formula out of pity, he didn’t need to lie to Mare, but he did. I’m sure Mare sees the bad side of everyone because of her job, and Frank’s lie would be pretty painful, I’m sure.
I like this show. I don’t see Mare as being bad at her job, I see her being pretty good at her job (finding the bullet, taking charge at the crime scene, being diligent) but she is cracking under pressure, and no one (except