I was under the impression that May initiated it immediately after the beserker staff thing to help Ward cope.

She initiated it then, but I took it as both of them wanting comfort since May was affected by the staff too. Afterwards though, it seemed like May was setting the terms of their fling entirely, -- she made comments about not letting it get personal, chewed Ward out for taking a punch for her, told Coulson without talking to him, and after Lorelei, she ends it without discussion. I'm not saying she's wrong for any of these things, but this doesn't seem like she was just trying to help him. And since Ward admitted he was only with her to help his mission, it seems unlikely she was helping him cope at all.

Yes, May did have the support of her husband after Bahrain, initially, but they drifted apart and separated

Which is heartbreaking, for sure, but given that he called to check up on her when Shield fell and came to help Skye when she asked, I'd say he's still really supportive. Plus, she has a loving mother who will drive hundreds of miles at the the drop of a hat for her, plus a friend like Coulson who, 7 years later, still believes in her and cares. So, even at the time of her greatest trauma, she has this tremendous support network. When you add that to the fact that she was already middle-aged and a highly trained professional, versus a child during his formative years with no other support system (since his primary givers were the ones causing the damage). I'm sorry, but the two just don't compare. It would be like Tony Stark telling Natasha she shouldn't have become an assassin because he didn't and he had a bad childhood too since his dad was distant and cold.

And I agree she doesn't air her baggage, but I guess I don't understand why it's relevant. Given that Ward used to keep his memories on lockdown, I think opening up about it might actually be a positive step for him.