The answer, for now, is that we don't exactly know why excessive amounts of omega 6s are bad. Excess dietary linoleic acid (LA) does not increase tissue arachidonic acid (AA) so the original (and simplistic) theory that more LA resulted in more AA-derived eicosanoids can't really be true. In fact, higher tissue AA may be beneficial.

It might be that excess LA simply prevents dietary alpha linolenic acid (ALA), an omega 3, from becoming EPA and, thereafter, EPA-derived eicosanoids. Since most people don't get much omega 3, the theory was that LA crowded out ALA for the enzymatic conversion (both are converted by the same enzyme, D6D) to the eventual end-products. This theory is probably too simple too, since piling omega 3 on top of a high LA diet does not seem to help as much as restricting LA in the first place. Plus, conjugated linoleic acid (CLA) a natural trans-fat from ruminant-animals, like cows, inhibits the conversion by D6D of both LA and ALA to their end-products. Nevertheless, CLA seems to reduce inflammation and may actually prevent cancer.

All we know now, I think, is that excessive dietary LA is modern (i.e., not paleo) and seems to cause "diseases of civilization" (e.g., cancer, heart disease, etc). It's probably a stretch to even say we "know" this - since concluding that LA causes disease is still controversial. Epidemiological studies go both ways (but recent results more often suggest LA is bad, especially in other countries where the confounding effects are probably lower than in the United States). There are a few well-constructed dietary trials (Lyon Diet Heart Trial, Veterans Trials) that seem to suggest LA causes disease as well. (And there are some trials that suggest the opposite, but these are generally less well constructed). Due to the lack of conclusive evidence, one's conclusions will depend on one's biases, where pro-modern, pro-establishment people will conclude LA is healthy (or at least not so bad) and naturalist-type, paleo people will conclude it's poison. Slowly the establishment consensus is shifting, in my opinion, in favor of the paleo people... I happen to believe the shit is poison and have for a quite a while.

EDIT: I forgot to mention evidence from animal and cell studies. It also suggests LA is bad shit.

Here's a nice visual of how dietary sources of PUFAs can result in the prostaglandins that affect inflammation (either pro or anti). At the risk of over-simplifying, PG1 and PG3 are generally anti-inflammatory, and PG2 is pro-inflammatory.

Dietary sources of AA are generally meat, while seed oils are sources of LA. But too much of the latter -- especially in the presence of higher insulin levels -- can result in dietary LA being converted to AA rather than the anti-inflammatory PG1 and thus to more of the pro-inflammatory PG2.