To put it another way:
Say you start reading a blog, on a subject that interests you. Half way through, the author starts talking about XYZ product, saying it really helped him out. The product sounds interesting, and it certainly sounds like it worked well for the author. But then you notice the link to the product is an affiliate link.
What do you think now? It may well be that the product was genuinely useful to the blog author, and it may well still be of interest to you, and you may still click it. But now you have a big warning sign in your head “maybe this guy just recommended the product because he gets paid if I buy it”
By contrast, if you had found the same link with no affiliate link, you would have no concern and you would believe that this author genuinely likes and recommends this product, with no ulterior motive. A non-affiliate link is therefore more valuable to your product-purchasing decision than an affiliate link; it is worth more “votes”.
You think all that because you are intelligent, and you have been around long enough to know that people often try and sell you things just to make money for themselves, and not because it will benefit you in any way. You know that there’s a chance the author just said it was great because he wants to make more money, not because it really is great.
Well guess what, Google is not dumb either, and they have been around a while too. It’s obvious to anyone that a reciprocal link has a strong likelyhood of an ulterior motive. Maybe the recommendation is still valid, but, just like the affid example above, it comes with a warning “this link exists not just for my benefit, but for their benefit too, treat it with a pinch of salt”. So its value is discounted – how much, who knows, but it’s not a trivial amount.
Having just read your reply, I think you are misunderstanding what I am saying. In particular:
I never said they shouldnt exist, and of course they will exist. There are numerous reasons why reciprocal links can and should exist in the real world, and I’m not saying they should be avoided too. I am talking purely about SEO. For SEO purposes, repcriocal links are worth very little. If you are obtaining links to boost your SE ranking, make sure they are oneway. If you are swapping links to boost direct click traffic, or just because it is a logical swap for your niche, go right ahead. You won’t be worse off than if you didn’t have those links, in SEO terms, you just won’t be much better off.
And it’s quite possible that google tracks 3 and 4 way links too, or will do in time. So that’s not a long-term business plan either. But generally it works ok for now.
To answer your other questions, yes I have done testing and no I won’t release the details. If you don’t believe me that’s quite all right and entirely up to you, I’m not trying to sell you anything here 
Just telling you what I know to be true, but what you believe is up to you and I don’t care either way.
Nothing wrong, sure. Just don’t expect to gain much of a SEO boost if the majority of your links are reciprocal rather than one-way. Which, as I keep saying, is entirely fair enough – oneway links indicate that someone, of their own free will and for no obvious ulterior motive, ‘voted’ for your site. I’m surprised you’d argue that point, it seems pretty obvious to me that natural linking should be worth much more than a manufactured (i.e. traded) linking. And we know Google has the money, the time, the knowledge and the inclination to keep improving its algorithm, so why would they not use this common sense measure?