When Agent May of the past is talking about the man she's been going on dates with, she mentions he's a shrink. This can be inferred that she was courting her future ex-husband, Andrew, who is a therapist.
Coulson's brush off of Ivanov's origin story and not remembering the object is reminiscent of Street Fighter (1994) when Raul Julia as Bison is talking to Ming-Na Wen as Chun-Li and says "I'm sorry my dear, I don't remember any of it. The day Bison graced your village was the most important day of your life, but for me, it was Tuesday."