Pregnancy and birth are very asymmetric, and then breastfeeding continues the pattern: nursing isn't going to be equitable. This means night feedings, more ability to calm the baby, and even just her smelling more familiar to them. While this asymmetry isn't permanent, it pushes you towards starting with an unequal division.

Then with parental leave it's very common for the mother to take more time off work than the father. Many jobs give more leave to birth parents, and someone who has just given birth often needs substantial recovery time. Fathers commonly earn more than mothers and so if leave is unpaid many couples can afford more if the mother takes it than if the father does.

If you're the dad, what can you do? I see two main aspects: sharing the work, and sharing the parenting.

From a work perspective, in as much as you want to be trying to make things fair you should be making up for the things you can't do by taking on more of the remaining work: non-feeding care, diapers, cooking, etc. Sleeping elsewhere sometimes so you have more energy and be more alert the next day can work well, as can taking the baby early in the morning so the mother can sleep in.

The other aspect is you want to be dividing the parenting, not just the work. This is because you really need to avoid a situation where the mother has a much better understanding of the baby than you do. For example, you can get into a cycle where you can't calm the baby as well, they spend more time with their mother, you get less experience and practice with them, and your relative abilities with the baby get farther and farther apart.

Having time when you're watching the baby solo is pretty valuable: you get practice much faster and your kid can't just insist on their preferred parent. My work gives (a very generous by US standards) twelve weeks of leave, which I took each time as two weeks at birth and ten after Julia went back to work. Having that time with the kids was great, both because I like them a lot but also because all that solo time set me on good footing for equal parenting later.

We've also found it useful to think through all the different aspects of parenting, both ones that take time and ones that take mental effort, and think about who's been doing them: when you go out who remembers to bring diapers, spare clothes, food? Who keeps track of medical appointments? Who does their baths? Who gets up in the night if they're crying? Who puts them to bed? Who arranges childcare? Splitting each individual task 50-50 loses a lot to coordination costs (more), but you can still split the tasks overall.

One pitfall here is that people will often assume that the mother is in charge of things related to the kids, and so judge her if they're not done well. If I were charge of the kids having clothes that are the right size and I didn't do a good job, other people wouldn't know that this was my responsibility.

While it doesn't cover everything, we've also found time tracking to be useful in checking that we're approximately balancing overall work (example). We'll take a representative couple weeks, see how our time shakes out, and compare.

One frame that can be useful is, if the mother had to suddenly take a 3-week trip, would you be ok with the kids on your own? If not, why not? Can you get to where you would be ok?

Another frame I've found useful is one I'm hesitant to describe: since people often get advice that's the opposite of what they should hear, consider that this might not be right for you. I've found trying to do substantially more of the parenting work to be a useful approach. This doesn't mean that I actually end up doing substantially more than my share, but if I were shooting for 50% I would likely fall short.

Overall, this is hard both because parenting is a lot of work but also because there's not much of an equal parenting script to go on. Chances are both parents grew up in households where the mother was responsible for more of the childcare, and models of balanced parenting are hard to find. Our division isn't perfect, but I hope thinking about some of this helps you end up being more the kind of parent and spouse you want to be.