I'm just curious as to why?
I had a brew before that turned out ok. I figured the boil kills off anything.
Well water is supposed to be the cleanest.
Well water can contain harmful bacteria and chemicals, and can have higher amounts of certain minerals than is wanted in brewing water.
We should focus on the minerals, since, as you say, we are boiling the water during the brewing process and therefore sanitizing (not sterilizing) the water so bacteria is not a concern. I'll leave chemicals off the discussion as well, since it is unlikely that you are drinking water that is considered harmful unless you live near fertilized farmland, a large factory, or a chemical plant AND have a shallow well.
To be the best, brewing water needs to meet certain mineral profile requirements. In general low to modest amounts of alkalinity are desired for pale beers, and moderate to moderately high amounts of alkalinity are best for dark beers. The acidity of the dark grains will help drop the pH into a range that is good for the mash (5.2-5.4)
High amounts of some minerals will affect the flavor. Iron can give a blood flavor. Sulfates and Chlorides are very often noted for affecting the taste of the beer. Sodium can give a salty flavor in excess.
The bottom line is that well water is just as likely to have an unwanted mineral makeup as water that comes from a municipal supply, even if it is likely to not have chlorine or chemicals deems unsafe at certain levels (But which are also unlikely to be tasted anyway.)
What a lot of brewers are doing these days is to send their water to Ward labs for a brewer's analysis so they can see how much of each mineral is in their water. A lot of them find the alkalinity of their water is high and not so great for mash pH in lighter colored beers, or even too high for dark beers!
If the alkalinity is high enough a lot of them (like me) generally just buy RO water and add the minerals amounts they want to match the style of beer they are brewing.
It's probably one of the more confusing areas of homebrewing for a lot of people, and one of the last things a homebrewer investigates in their progression through the hobby.
So the point is that although your well water is likely to have less chemicals in it than water from a municipal supply, there is no guarantee it's chemical free, and it may have bacteria in it as well that won't harm you, but in a beer can spoil it. It may also have more than desired amounts of certain minerals or alkalinity to be best for brewing.
Also note that a lot of people don't care to delve into water analysis and adjustments. They like the flavor of their beer just fine and that's ok. Not everyone has to be a nerd when it comes to brewing.
