One the reasons I knew my husband was a great partner for me is because he respects my boundaries and knows how to be supportive without being pushy or bossy. This really should be a super obvious, basic thing, but it's apparently startlingly difficult for many straight, cisgender men, because patriarchy. That can be a huge problem for straight, co-parenting couples, where dads quite admirably want to be involved in all aspects of parenting, but don't understand that there are times when dads should actually back off.
When I say "back off" here, I don't mean "disengage completely." I mean "follow someone else's lead, instead of trying to set the agenda." That can be challenging for people who have been socialized to believe that they should always be in charge or always take an active role in everything, rather than a supporting one. If you spend more than a day in any online mom group, for example, you'll inevitably see thread after thread of rants and requests for advice because of problems caused by dads who don't understand that, in some situations, it's just not their place or their right to make the call. (That's not to say that this dynamic doesn't or can't pop up in queer parenting relationships, but because straight couples are both more common and more subject to the pitfalls of toxic masculinity, dads who overstep their boundaries with moms are a more common problem than the reverse.)
There is so much to parenting, and so many opportunities to bond and be involved, so dads and those who love them shouldn't worry that backing off in any of the following situations means they can't or shouldn't be involved in anything. (On the flip side, men who use the fact that they can't call all the shots as an excuse to do nothing are putting up a giant red flag; namely that they're either looking for an excuse to be uninvolved, or that they're controlling. Please: if someone is trying to control you or pressure you to do anything you're not OK with, keep an eye out for other signs of abusive relationship dynamics and get help if you need to.) Recognizing when to step up and step back is important for everyone, especially in parenting. Since learning that can be harder for some than others, here's a cheat sheet for dads who don't always realize when they're crossing the line.