Confidence.
Unless you have been home educated yourself, this is a new way to look at schooling most likely, and much of what makes it challenging is simply believing that the only way to learn is with a teacher.
Questioning.
Is homeschooling legal?
How do they make friends?
Shouldn't you be in school?
Are you a teacher?
How will you do year 12? (particularly hilarious when the child is 7 and has 11 more years before year 12!)
All these questions can be exhausting for a newby homeschooler, and tbh perfectly unnecessary. Some of them come from curiousity and a desire to understand, and some are simply because people disagree. I barely encounter them anymore, and I think it's simply because I've been home educating so long and I know it works.
Deschooling
Transforming a parent from a schooled adult to an educated adult, can be as challenging as deschooling a child. In our case most of the deschooling process wasn't too burdensome, given DD23 didn't attend school for very long. For myself, I realised I was still deschooling my art school education a couple of years ago. We were encouraged for all art to be large, and I simply didn't have time for that. After doing an online sketch book course with DS21, I started carrying small sketchbooks, and felt totally liberated. I love doing art- but my projects at this stage of life need to be small, due to time constraints.
Babies
Home education and babies are challenging. For both my younger two, we took time off for between 6weeks to 3 months. DS15 is a Summer baby so that naturally aligned with our Summer break. DS10 is a Winter baby, and the longer break turned into a permanent thing around here, because we all felt refreshed from taking 6weeks mid-year (normal here is 2 weeks).
Also for a couple of years we live in what I call baby rhythm, where the baby is prioritised first, and activities are organised around the baby somewhat. Around here that might mean we wouldn't follow our usual routine when tired. We might drop activities when tired. We would read together in bed with the baby. Babies bring a lot of chaos but also a lot of fun, and one of my favourite aspects is that everyone in the family gets to understand babies.
Unfamiliar Topics/ Weak Areas
Anything that is a challenging topic- due to inexperience, ignorance or feeling a failure- there will be a class, a teacher or a mentor for. The common topic that people feel underqualified for is maths- so I've been asked about it a lot. It is not an issue for me- but there are loads of options online, as well as with books. For me the first topic that was a challenge was music. As well as learning alongside my kids, we paid for classes, and DD23 and DS21 attended choir in Adelaide. DD23 went on to learn Suzuki violin with DH@damienjbyrne and continued from there. Damien did have quite a bit of experience with music, but lacked confidence with it, and with these beginnings DD23 eventually progressed with continued musical education to studying a Diploma in Music Industry at University for her final high school year.
Alone Time
If your family are supportive and local this will make the early years much easier. It is exhausting needing to be in a 24hour a day giving roll. If you've got a few children it does go on for years, and you need to find ways to recharge. Once past the early years things begin to change. Children can be left at home, older children can babysit younger children, older children can get themselves to class, pick things up from the shop, help with dinner, and have interesting conversations.
None of these challenges are insurmountable, but there will be times when you wonder if you can keep doing it, and having a supportive family and a community of home educators around you where you can express your frustrations will make continuing much easier.
https://www.cantrip.org/gatto.html
"The six lesson school teacher", a great article, covering what school actually teaches your child.