Why is the highest marginal tax rate in the US 39.6% while all others are rounded?
In 2001, tax rates were changed again, eventually dropping to 35%. Then they went back up in 2013. But the next lower rate, 35%, did not increase (2016 rates).
The literal answer to your question is that it was the only rate formed by adding a surcharge to a lower rate. Perhaps that is deemed acceptable for the higher income people in that bracket where lower income people get integral rates. It's not a surcharge anymore, but the effective rate is now the same as before the Bush tax cuts.
It's also an artifact of the deal made. Without any deal at the end of 2012, the Bush tax cuts would have expired and returned everything to the 2000 rates. By accepting that change for just the people in that bracket, they preserved 75% of the Bush tax cuts. One side opposed a lower rate like 39% and the other opposed 40%. Taking the 39.6% that they would have had with no deal was their compromise.