Brain surgery! Definitely a bad idea as a DIY project.
Seriously, I think there are few such things that can DEFINITELY be put on a non-DIY list or not. For one individual, changing a light bulb may be a stretch. For another person, tearing out a complete kitchen and redoing it, building the cabinets from scratch, is all a simple thing.
Years ago when I was faced with my very first attempt at a plumbing repair, I was worried I would burn down the house when I fired up the propane torch. So I did some research, talked to a few people with more experience. It went off without a hitch. The point is to do the necessary research in advance if you have no experience, and if you will be doing it yourself.
Of course, the presence of a mentor who can guide you through the tricky steps is incredibly valuable. This is one way that web sites like this prove useful. They offer a way to get that mentoring for a DIY newbie, from someone who has gone through the learning process already.
There is one other factor in the DIY scheme of things - the possession of the right tools for the job. For example, in my younger years I was willing to do things like replace the muffler on my car. After a while, I found that while this is something I am capable of doing as a DIY project, it simply is not worth several hours of my time, getting junk in my eyes while laying on my back underneath the car. A better choice for me is to pay someone to put the car up on a lift and do the job quickly, with better tools than I possess. Or, perhaps I might tell you of the miserable day I spent on a brake job on my car in the middle of winter, done in a windy parking lot.
What I learned was that I simply don't enjoy doing work like that, even if I am capable of doing it. I learned that for ME, a good DIY job is one that I have the skills to do, or where I can easily enough learn the skills needed. It is one where I have the tools I need, or the tools are inexpensive enough to buy or rent. A DIY job is one where I can do it myself for significantly less money than I can pay someone else to do it for me. And all of these factors will be different for every person out there.
My strategy over the years has been to learn my capabilities for such work, and what I like to do. Then as I need to do one project or another, to buy the necessary tools if I will use them more than twice. Use a tool once, I'll borrow it or rent it if I can. Gradually you build up the capability to DIY for many of the problems you will find around the house.