As if mothers, throughout history, haven't had to just get on with it without being allowed such excuse
Becuase of course the fairer sex have never had to take their time in terms of the gear change from non parent to parent. Even when their gear change is one of all day, everyday, rather than fits and starts. With somebody poking their head in now and then to critise.
This doesn't necessarily have everything to do with being be-penised or not, possibly more to do with being very unused to taking charge of resident smallie, and when not being in charge feeling like a spare wheel that can't live up to the expertise of the primary carer so withdraws from active duty.
Dad care might not look like mum care if reading widower's blog are anything to go by, but given the chance to create a habit, without "constuctive critisim" lurking behind a door most men are more than able toick up the reins and run with, once they've cut their teeth and got round what looks like onerous logistics to the uninitiated.
And it is his child too.
If mums want dads to be more involved they can't retain the control and say how the care should be coloured (bar neglect and dangerous things), cos tjat is cake and eat it. You are just as much a parent as me but thou shalt do it my way, sort of thing.
The dads have to carve out their own priorities, get used to doing stuff (like showers) whilst being in sole charge (that one really stumped me once DS got mobile), work out what works and what doesn't. None of which is going to happen unless they are allowed to get with their learning curve without somebody jarrying them saying "hurry up' and be a carbon copy of me while you are at it".
My DH didn't pick up his game till I stopped poking my nose in. and he had the advanatage of doing it all day, everyday not here and there.
For all my hand waving, chastisment and worry that Monsters Inc twice a day was going to rot both their brains for that period when DH was peimary carer in the day, almost a decade on they have a hugely close relationship, do all sorts of outdoorsy sporty stuff together and quite frankly
eave me out much of the time.
Niether of them have turned into drooling braindead persons glued to the telly either.
Give the guy a break, he sounds willing, let him work it out, don't make him feel inadequate or undermined with constuctive critism, make it a more regular event so he gets the practice which helps create a sense of familiarity with the logistics, stand back and watch him BE the equally responsible parent he is, in his own style, rather than just using the term in an accusatory fashion.
Then whinge like hell when you get your nose put of joint cos Daddy is the most favoritest person in the whole wide world 
Bit the above is far easier to say than do. God knows I used to stalk in and start huffily dressing DS in actual clothes, switch off the telly and ostentaciously make him finger paint to prove a point.
With much dark muttering about lazy arsed fathers who I couldn't trust with the mental stimulation of a cat let alone my PFB.