Google is using links from other sites to work out what sites are popular. It takes a link as a vote: “this site provides useful information on the subject of
A reciprocal link defeats that object. It’s not a vote of confidence. It’s a vote of “I’ll vote for you if you vote for me”. It tells Google that you don’t hugely care what is on the site you link to, you only care that they link back to you.
It’s common sense that reciprocal links should be no (or little) good, and it’s also common fact borne out of testing. Exactly how much they are valued or discounted is unknown, but they certainly aren’t anywhere near as good as one way links.
If you want to swap links, do 3 or 4 way linking to hide it somewhat. It’s just daft doing it directly.