Two examples come to mind.
When we had a faucet that was broken, or rather, it kept breaking, because of poor construction at the diverter.
When I wanted a stand for my cell phone.
It costs almost nothing. Well, it cost less for sure. The faucet cost the cost of the faucet and the time to put it together. But the putting it together is nice time, it is a benefit, you are working. You are improving yourself and your skills. The cell phone stand cost three pieces of scrap wood and four shingle nails.
Summary: Cost may be minimized
You get stuff faster.
I mean I did the faucet likely slower than a professional because I had not done it before. Not sure about the tools and how it all went together. A professional can get it done faster or on the first try, but there is scheduling with the professional. And there is also time that is spent getting the funds to pay the professional. Suddenly an $80 faucet, plus expertise and labor, plus the time it took to get the money to pay the person, well that starts to add up to a lot of time. At some point, when the iron is hot, this trade-off is worth it. But often you are operating at a razor edge at that point anyway.
The cell phone stand, I thought about it, and then it was made in 15 minutes, maybe I procrastinated on it and thought about it for another 15 minutes before I actually did it.
Faster than two-day delivery from Amazon, faster than shipping from China, faster than work on etsy.
Summary: You get the goods faster.
You have a chance to make it exactly what you want for the price you want.
The faucet is exactly what we wanted for the price we wanted, aesthetically pleasing and durable.
The cell phone stand is exactly the width.
You gain skills.
The faucet was an opportunity to learn something.
I can replace another faucet in the future, easier and faster. I can discuss with an expert more readily in terms he might understand. I can even do the faucet for other people, thereby providing a service and value.
The cell phone stand is a good cell phone stand. I can make another to suit my needs differently.
Summary: You enhance your future capacity to do the job in the future, communicate the job with a professional, do the job for others.
Do it yourself is a lifechanging outlook.
Once you realize you can do this small job yourself, you realize that many things in life can be broken down into blocks to put together.