As others have said, "doing your taxes" doesn't necessarily have anything to do with paying your taxes. It's more like balancing a checkbook.
I have almost the simplest tax situation that you can have in the US, so I have always used the free tax preparation software that some places make available to file federal taxes. However, even I end up with slight complexities in my taxes each year because I do have an interest-bearing account (and thus significant, though not substantial, interest income), and my husband has been a graduate student for many years. His income has been intermittent, and we have sometimes had to pay his tuition (which is generally a deductible expense).
This year, for the first time, I finally paid the same tax preparation software to file my state income taxes, too, even though the return is not all that hard to fill out. It's hard enough that I usually have to do it 2 or 3 times before I can get the numbers right, and I decided that spending $30 to have somebody else just do it for me was more than worth the time I would save not having to do it myself. At least in my state, income taxes are rendered slightly more complicated by the fact that I have to determine what my federal tax liability is (which isn't necessarily the same as the federal taxes I owed or paid), because I can deduct that from my taxable income for state income tax purposes. I usually do that calculation wrong at least 5 or 6 times every year, because the instructions aren't very good.
My parents are probably reasonably typical for a middle class household, but have been using an accountant to file their taxes for as long as I can remember. They did used to have rental income (though they don't anymore), and they have always had significant investments (to save for my and my siblings' college educations and to save for their own retirement), so I think that rendered their taxes sufficiently complicated that they didn't want to do them themselves. I am pretty sure it's not a lack of ability, in the end, but a difference in approach. In other words, paying an accountant saves them fighting about how they should be doing their taxes for months each year, so it's worth it to them.
I can understand that completely, even though I hadn't ever paid anyone to do any part of my taxes before this year. But even though my husband is very capable (he filed his own taxes for years before we got married, and his were crazy complicated because he was a foreign national here on a student visa), we have very different approaches to how we do things like this. So I file our taxes basically without his involvement (he hands me the forms and I tell him a sort of summary when I'm finished), largely because I mind it less than he would and it's one of my contributions towards our household. But when filing our taxes gets to be too difficult or too time consuming for me to be willing to do it on my own, that's when I'll either start paying for software that can handle the added complexity, or just flat-out hiring an accountant. This is not an area where my husband would be able to help me (or I would be able to help him), because we'd just end up fighting about it.